Find the smallest whole number by which 6912 should be multiplied to make a perfect square
Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 3 Squares And Square Roots are provided here with simple step-by-step explanations. These solutions for Squares And Square Roots are extremely popular among Class 8 students for Math Squares And Square Roots Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 3 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate. Show Page No 42:Question 1:Using the prime factorisation method, find which of the following numbers are perfect squares: Answer:A perfect square can always be expressed as a product of equal factors. (i) Thus, 441 is a perfect square. (ii) Thus, 576 is a perfect square. (iii) Thus, 11025 is a perfect square. (iv) 1176 cannot be expressed as a product of two equal numbers. Thus, 1176 is not a perfect square. (v) Thus, 5625 is a perfect square. (vi) 9075 is not a product of two equal numbers. Thus, 9075 is not a perfect square. (vii) Thus, 4225 is a perfect square. (viii) Thus, 1089 is a perfect square. Page No 42:Question 2:Show that each of the following numbers is a perfect square. In each case, find the number whose square is the given number: Answer:A perfect square is a product of two perfectly equal numbers. (i) 1225=25×49=5×5×7×7=5×7×5×7=35×35=(35)2 Thus, 1225 is the perfect square of 35. (ii) Thus, 2601 is the perfect square of 51. (iii) 5929=11×539=11×7×77=11×7×11×7=77×77=(77)2 Thus, 5929 is the perfect square of 77. (iv) Thus, 7056 is the perfect square of 84. (v) 8281=49×169=7×7×13×13=7×13×7×13=(7×13)2=(91)2 Thus, 8281 is the perfect square of 91. Page No 42:Question 3:By what least number should the given number be multiplied to get a perfect square number? In each case, find the number whose square is the new number. Answer:1. Resolving 3675 into prime factors: Thus, to get a perfect square, the given number should be multiplied by 3. New number= (32×52×72)=(3×5×7)2 =(105)2 Hence, the new number is the square of 105. 2. Resolving 2156 into prime factors: Thus to get a perfect square, the given number should be multiplied by 11. New number =(22×72×112)=(2×7×11)2=(154)2 Hence, the new number is the square of 154. 3. Resolving 3332 into prime factors: Thus, to get a perfect square, the given number should be multiplied by 17. New number =(22×72×172)=(2×7×17)2=(238)2 Hence, the new number is the square of 238. 4. Resolving 2925 into prime factors: Thus, to get a perfect square, the given number should be multiplied by 13. New number =(32×52×132 )=(3×5×13)2=(195)2 Hence, the number whose square is the new number is 195. 5. Resolving 9075 into prime factors: 9075=3×5×5×11×11=3 ×52×112 Thus, to get a perfect square, the given number should be multiplied by 3. New number =(32×52×112)=(3×5×11)2 =(165)2 Hence, the new number is the square of 165. 6. Resolving 7623 into prime factors: Thus, to get a perfect square, the given number should be multiplied by 7. New number =(32×72×112)=(3×7×11)2=(231)2 Hence, the number whose square is the new number is 231. 7. Resolving 3380 into prime factors: Thus, to get a perfect square, the given number should be multiplied by 5. New number =(22×52×132)=(2×5×13)2=(130)2 Hence, the new number is the square of 130. 8. Resolving 2475 into prime factors: Thus, to get a perfect square, the given number should be multiplied by 11. New number =(32×5 2×112)=(3×5×11)2=(165)2 Hence, the new number is the square of 165. Page No 42:Question 4:By what least number should the given number be divided to get a perfect square number? In each case, find the number whose square is
the new number. Answer:(i) Resolving 1575 into prime factors: Thus, to get a perfect square, the given number should be divided by 7 New number obtained=(32×52)=(3×5)2=(15)2 Hence, the new number is the square of 15 (ii) Resolving 9075 into prime factors: 9075=3×5×5×11×11=3×52×112 Thus, to get a perfect square, the given number should be divided by 3 New number obtained=(52 ×112)=(5×11)2=(55)2 Hence, the new number is the square of 55 (iii) Resolving 4851 into prime factors: 4851=3×3×7×7×11= 32×72×11 Thus, to get a perfect square, the given number should be divided by 11 New number obtained=(32×72)=(3×7)2=(21) 2 Hence, the new number is the square of 21 (iv) Resolving 3380 into prime factors: 3380=2×2×5×13×13=22×5×132 Thus, to get a perfect square, the given number should be divided by 5 New number obtained=(22×132)=(2×13)2=(26)2 Hence, the new number is the square of 26 (v) Resolving 4500 into prime factors: 4500= 2×2×3×3×5×5×5=22×32×52×5 Thus, to get a perfect square, the given number should be divided by 5 New number obtained=(22× 32×52)=(2×3×5)2=(30)2 Hence, the new number is the square of 30 (vi) Resolving 7776 into prime factors: 7776=2×2×2× 2×2×3×3×3×3×3=22×22×2×32×32×3 Thus, to get a perfect square, the given number should be divided by 6 whish is a product of 2 and 3 New number obtained=(22×22×32×32)=(2×2×3×3)2=(36)2 Hence, the new number is the square of 36 (vii) Resolving 8820 into prime factors: 8820=2×2×3×3×5×7×7=22×32×5×72 Thus, to get a perfect square, the given number should be divided by 5 New number obtained=(22×32×72)=(2×3×7)2=(42)2 Hence, the new number is the square of 42 (viii) Resolving 4056 into prime factors: 4056=2×2×2×3×13×13=22×2×3×132 Thus, to get a perfect square, the given number should be divided by 6, which is a product of 2 and 3 New number obtained =(22×132)=(2×13)2=(26)2 Hence, the new number is the square of 26 Page No 42:Question 5:Find the largest number of 2 digits which is a perfect square. Answer:The first three
digit number (100) is a perfect square. Its square root is 10. Page No 42:Question 6:Find the largest number of 3 digits which is a perfect square. Answer:The largest 3 digit number is 999. The number whose square is 999 is 31.61. Thus, the square of any number greater than 31.61 will be a 4 digit number. 312=31×31=961 Page No 45:Question 1:Give reason to
show that none of the numbers given below is a perfect square: Answer:By observing the properties of square numbers, we can determine whether a given number is a square or not. (i) 5372 (ii) 5963 (iii) 8457 (iv) 9468 (v) 360 (vi) 64000 (vii) 2500000 Page No 45:Question 2:Which of the following are squares of even numbers? Answer:The square of an even number is always even. (i) 196 (ii) 441 (iii) 900 (iv) 625 (v)
324 Page No 46:Question 3:Which of the following are squares of odd numbers? Answer:According to the property of squares, the square of an odd number is also an odd number. (i) 484. (ii) 961 (iii) 7396 (iv) 8649 (v) 4225 Page No 46:Question 4:Without adding, find the sum: Answer:Sum of first n odd numbers = n2 (i) (1+3+ 5+7+9+11+13) = 72=49 (ii) (1+3+5+7+9+11+13+15+17+19)=10 2=100 (iii) (1+3+5+7+9+11+13+15+17+19+21+23) = 122 = 144 Page No 46:Question 5:(i) Express 81 as the sum of 9 odd numbers. Answer:Sum of first n odd natural numbers = n2 (i) Expressing 81 as a sum of 9 odd numbers: (ii) Expressing 100 as a sum of 10 odd numbers: Page No 46:Question 6:Write a pythagorean triplet whose smallest member is Answer:For every number m > 1, the Pythagorean triplet is 2m, m2-1, m2+1. Using the above result: (i) Thus, the Pythagorean triplet is 6,8,10. (ii) Thus, the Pythagorean triplet is 14,48,50 . (iii) Thus, the Pythagorean triplet is: 16,63,65 (iv) Thus, the Pythagorean triplet is 20,99 ,101. Page No 46:Question 7:Evaluate: Answer:Given: n+12-n2 = n+1+n (i) 382-37 2=38+37=75 (ii) 752-742=75+74=149 (iii) 922-91 2=92+91=183 (iv) 1052-1042=105+104=209 (v) 1412-140 2=141+140=281 (vi) 2182-2172=218+217=435 Page No 46:Question 8:Using the formula (a + b)2 = (a2 +
2ab + b2), evaluate: Answer:(i) 3102=300+102=3002+2300×10 +102=90000+6000+100=96100 (ii) 5082=500+82=5002+2500×8 +82=250000+8000+64=258064 (iii) 6302=600+302=6002+2600×30 +302=360000+36000+900=396900 Page No 46:Question 9:Using the formula (a − b)2 = (a2 − 2ab + b2), evaluate: Answer:(i) 1962=200-42=2002-2200×4+42=40000-1600+16=38416 (ii) 6892=700-112=7002-2700×11+112=490000-15400+121=474721 (iii) 8912=900-92=9002-2900×9+92=810000-16200+81=793881 Page No 46:Question 10:Evaluate: Answer:(i) 69×71=70-1×70+1=702-12=4900 -1=4899 (ii) 94×106=100-6×100+6=1002-62=10000-36=9964 Page No 46:Question 11:Evaluate: Answer:(i) 88×92=90-2×90+2=902-22 =8100-4=8096 (ii) 78×82=80-2×80+2=802-22=6400-4=6396 Page No 46:Question 12:Fill in the blanks: Answer:(i) The square of an even number is even. (ii) The square of an odd number is odd. (iii) The square of a proper fraction is smallerthan the given fraction. (iv) n2=the sum of first n oddnatural numbers. Page No 46:Question 13:Write (T) for true and (F) for false for each of the statements given below: Answer:(i) F (ii) F (iii) F (iv) F (v) T Page No 48:Question 1:Find the value of using the column method: Answer:Using the column method:
∴ 232=529 Page No 48:Question 2:Find the value of using the column method: Answer:Using the column method:
∴ 352 = 1225 Page No 48:Question 3:Find the value of using the column method: Answer:Using the column method: Here, a = 5 ∴ 522=2704 Page No 48:Question 4:Find the value of using the column method: Answer:Using column method: Here, a =9b = 6
∴ 962=9216 Page No 49:Question 5:Find the value of using the diagonal method: Answer:672=4489 Page No 49:Question 6:Find the value of using the diagonal method: Answer:862=7396 Page No 49:Question 7:Find the value of using the diagonal method: Answer:1372=18769 Page No 49:Question 8:Find the value of using the diagonal method: Answer:2562=65536 Page No 50:Question 1:Find the square root of number by using the method of prime factorisation: Answer:
By prime factorisation method: 225=3×3×5×5225=3×5=15 Page No 50:Question 2:Find the square root of number by using the method of prime factorisation: Answer:By prime factorisation: 441=3×3×7×7 ∴ 441=3×7=21 Page No 50:Question 3:Find the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 729=3×3×3×3×3×3 ∴ 729 =3×3×3=27 Page No 50:Question 4:Find the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 1296=2×2×2×2 ×3×3×3×3 ∴1296=2×2×3×3=36 Page No 50:Question 5:Find the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 2025=3×3×3×3×5×5 ∴2025=3×3×5=45 Page No 50:Question 6:Find the square
root of number by using the method of prime factorisation: Answer:Resolving into prime factors: ∴ 4096=2×2×2×2×2×2=64 Page No 50:Question 7:Find the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 7056=2×2×2×2×3×3×7×7 ∴7056=2×2×3×7=84 Page No 50:Question 8:Find
the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 8100=2×2×3×3×3×3×5×5 ∴8100= 2×3×3×5=90 Page No 50:Question 9:Find the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 9216=2×2×2×2 ×2×2×2×2×2×2×3×3 ∴ 9216=2×2×2×2×2×3=96 Page No 50:Question 10:Find the square root
of number by using the method of prime factorisation: Answer:Resolving into prime factors: 11025=3×3×5×5×7×7 ∴11025=3×5×7 =105 Page No 50:Question 11:Find the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 15876=2×2×3×3×3×3×7× 7 ∴15876=2×3×3×7=126 Page No 50:Question 12:Find the square root of number by using the method of prime factorisation: Answer:Resolving into prime factors: 17424=2×2×2×2×3×3×11×11 ∴ 17424=2×2×3×11=132 Page No 50:Question 13:Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained. Answer:Resolving into prime factors: 252=2×2×3×3×7 Thus, the given number must be multiplied by 7 to get a perfect square. New number = 252×7=1764 ∴1764=2×3×7=42 Page No 50:Question 14:Find the smallest number by which 2925 must be divided to obtain a perfect square. Also, find the square root of the perfect square so obtained. Answer:Resolving into prime factors: 2925=3×3×5×5×13 13 is the smallest number by which the given number must be divided to make it a perfect square. New number = 2925÷13=225 225=3×5=15 Page No 50:Question 15:1225 Plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row. Answer:Let the number of rows be x. Thus, the number of rows is 35 and the number of plants in each row is 35. Page No 50:Question 16:The students of a class arranged a picnic. Each student contributed as many rupees as the number of students in the class. If the total contribution is Rs 1156, find the strength of the class. Answer:Let the number of students be x. Total amount contributed =x×x=x2=1156 1156=2 ×2×17×17x=1156=2×17=34 Thus, the strength of the class is 34. Page No 50:Question 17:Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20. Answer:The smallest number
divisible by each of these numbers is their L.C.M. Resolving into prime factors: Required number = 180×5=900 Page No 51:Question 18:Find the least square number which is exactly divisible by each of the numbers 8, 12, 15 and 20. Answer:The smallest number divisible by each of these numbers is their L.C.M. Resolving into prime factors: To make this into a perfect square, we need to multiply the number with 2×3×5=30. Required number = 120×30=3600 Page No 54:Question 1:Evaluate: Answer:Using the long division method: ∴ 576 = 24 Page No 54:Question 2:Evaluate: Answer:Using the long division method:
∴ 1444 = 38 Page No 54:Question 3:Evaluate: Answer:Using the long division method: ∴ 4489 = 67 Page No 54:Question 4:Evaluate: Answer:Using the long division method:
∴ 6241 = 79 Page No 54:Question 5:Evaluate: Answer:Using the long division method:
∴ 7056 = 84 Page No 54:Question 6:Evaluate: Answer:Using the long division method:
∴ 9025 = 95 Page No 54:Question 7:Evaluate: Answer:Using the long division method:
∴ 11449=107 Page No 54:Question 8:Evaluate: Answer:Using the long division method: ∴ 14161=119 Page No 54:Question 9:Evaluate: Answer:Using the long division method:
∴ 10404=102 Page No 54:Question 10:Evaluate: Answer:Using the long division method: ∴ 17956 = 134 Page No 54:Question 11:Evaluate: Answer:Using the long division method:
∴ 19600=140 Page No 54:Question 12:Evaluate: Answer:Using the long division method:
∴ 92416=304 Page No 54:Question 13:Find the least number which must be subtracted from 2509 to make it a perfect square. Answer:Using the long division method:
Therefore, the number that should be subtracted from the given number to make it a perfect square is 9. Page No 54:Question 14:Find the least number which must be subtracted from 7581 to obtain a perfect square. Find this perfect square and its square root. Answer:Using the long division method:
Therefore, the number that should be subtracted from the given number to make it a perfect square is 12. Perfect square = 7581-12 = 7569 Its square root is 87. Page No 54:Question 15:Find the least number which must be added to 6203 to obtain a perfect square. Find this perfect square and its square root. Answer:Using the long division method:
Thus, to get a perfect square greater than the given number, we take the square of the next natural number of the quotient, i.e. 78. 792=6241 Number that should be added to the given number to make it a perfect square =6241-6203=38 The perfect square thus obtained is 6241 and its square root is 79. Page No 54:Question 16:Find the least number which must be added to 8400 to obtain a perfect square. Find this perfect square and its square root. Answer:
Using the long division method:
The next natural number that is a perfect square can be obtained by squaring the next natural number of the obtained quotient, i.e. 91. Therefore square of (91+1) = 922=8464 Number that should be added to the given number to make it a perfect square =8464-8400=64 The perfect square thus obtained is 8464 and its square root is 92. Page No 54:Question 17:Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained. Answer:Smallest number of four digits =1000 Using the long division method:
1000 is not a perfect square. By the long division method, the obtained square root is between 31 and 32. Squaring the next integer (32) will give us the next perfect square. 322=1024 Thus, 1024 is the smallest four digit perfect square. Also, 1024=32 Page No 54:Question 18:Find the greatest number of five digits which is a perfect square. Also find the square root of the number so obtained. Answer:Greatest number of five digits =99999 Using the long division method:
99999 is not a perfect square. 3162=99856 99856 is the required number. Page No 54:Question 19:The area of a square field is 60025 m2. A man cycles along its boundary at 18 km/h. In how much time will he return to the starting point? Answer:Area of the square field = 60025 m2 = 980
1000 km Time = Distance travelledSpeed = 980100018 = 9801000 × 18 hr =980 × 60 × 6018000 sec =98 × 2 sec = 196 sec = 3 min 16 sec Page No 56:Question 1:Evaluate: Answer:Using long division method:
∴ 1.69=1.3 Page No 56:Question 2:Evaluate: Answer:Using long division method:
∴ 33.64=5.8 Page No 56:
Question 3:Evaluate: Answer:Using long division method: ∴ 156.25=12.5 Page No 56:Question 4:Evaluate: Answer:Using long division method: ∴ 75.69=8.7 Page No 56:Question 5:Evaluate: Answer:Using long division method:
∴ 9.8596=3.14 Page No 56:
Question 6:Evaluate: Answer:Using long division method:
∴ 10.0489=3.17 Page No 56:Question 7:Evaluate: Answer:Using long division method: ∴ 1.0816=1.04 Page No 56:Question 8:Evaluate: Answer:Using long division method: ∴ 0.2916=0.54 Page No 56:Question 9:Evaluate 3 up to two places of decimal. Answer:Using long division method:
3=1.732 ⇒3 = 1.73 (correct up to two decimal places) Page No 56:Question 10:Evaluate 2.8 correct up to two places of decimal. Answer:Using long division method: ∴ 2.8=1.673 ⇒2.8 =1.67 (correct up to two decimal places) Page No 56:Question 11:Evaluate 0.9 correct up to two places of decimal. Answer:Using long division method:
∴ 0.9=0.948 ⇒0.9 =0.95 ( correct up to two decimal places) Page No 56:Question 12:Find the length of each side of a square whose area is equal to the area of a rectangle of length 13.6 metres and breadth 3.4 metres. Answer:Area of the rectangle =(13.6 × 3.4) =46.24 sq
m Length of each side of the square = 46.24 m Using long division method:
46.24=6.8 Thus, the length of a side of the square is 6.8 metres. Page No 58:Question 1:Evaluate: Answer:16 81=1681 16 = 4 and 81 = 9 ∴ 1681= 1681=49 Page No 58:Question 2:Evaluate: Answer:64225= 64225 Using long division method: 225=15
∴ 64225=64225=815 Page No 58:Question 3:Evaluate: Answer:121256=121256 Using division method: 121=11
∴121256=121256=1116 Page No 58:Question 4:Evaluate: Answer:625729=625729 Using long division method:
625=25
729=27 ∴625729=625729= 2527 Page No 58:Question 5:Evaluate: Answer:31336=12136=12136=11×116×6 =116=1511 Page No 58:Question 6:Evaluate: Answer:473324=1369324=1369324 Using long division method: 324 = 2×2×9×9 = 2×9 = 18 ∴473324=3718=2118 Page No 58:Question 7:Evaluate: Answer:333289=900289=900289 Using long division method:
289=17 And 900 = 2×2×5×5×3×3 = 2×5×3 = 30 ∴ 333289=3017=11317 Page No 58:Question 8:Evaluate: Answer:We have: 80405=80405=1681= 1681=49 Page No 58:Question 9:Evaluate: Answer:We have: 11832023=11832023= 169289= 169289=13×1317×17=1317 Page No 58:Question 10:Evaluate: Answer:We have: 98×162=98×162 =2×7×7×2×9×9=2×7×9=126 Page No 58:Question 1:Tick
(✓) the correct answer Answer:(c) 5478 According to the properties of squares, a number ending in 2, 3, 7 or 8 is not a perfect square. Page No 58:Question 2:Tick (✓) the correct answer Answer:(d) 2222 According to the property of squares, a number ending in 2, 3, 7 or 8 is not a perfect square. Page No 58:Question 3:Tick (✓) the correct answer Answer:(a) 1843 Page No 58:Question 4:Tick (✓) the correct answer Answer:(b) 4787 By the property of squares, a number ending in 2, 3,7 or 8 is not a perfect square. Page No 58:Question 5:Tick (✓) the correct answer Answer:(c) 81000 According to the property of squares, a number ending in odd number of zeroes is not a perfect square. Page No 58:Question 6:Tick (✓) the correct answer Answer:(d) 8 According to the property of squares, a perfect square cannot have 2, 3, 7 or 8 as the unit digit. Page No 58:Question 7:Tick (✓) the correct answer Answer:(b) smaller than the fraction Page No 58:Question 8:Tick (✓) the correct answer Page No 58:Question 9:Tick (✓) the correct answer Answer:(d) (8,15,17) This can be understood from the property of Pythagorean triplets. According to this property, for a natural number m, (2m, m
2-1, m2+1) is a Pythagorean triplet. Page No 58:Question 10:Tick (✓) the correct
answer Answer:Page No 58:Question 11:Tick (✓) the correct answer Answer:Page No 59:Question 12:Tick (✓) the correct answer Answer:(b) 6 15370+6=1537615376=124 Page No 59:Question 13:Tick (✓) the correct answer Answer:(d) 0.94
0.9=0.94 Page No 59:Question 14:Tick (✓) the correct answer Answer:(c) 0.316 Using long division method:
∴ 0. 1= 0.316 Page No 59:Question 15:Tick (✓) the correct answer Answer:Page No 59:Question 16:Tick (✓) the correct answer Answer:(c) 32 288128=288128=2×2 ×2×2×2×3×32×2×2×2×2×2×2=3×32×2=3×32×2 =32 Page No 59:Question 17:Tick (✓) the correct answer Answer:Page No 59:Question 18:Tick (✓) the correct answer Answer:(a) 196 Square of an even number is always an even number. Page No 59:Question 19:Tick (✓) the correct answer Answer:(c) 1369 Square of an odd number is always an odd number. Page No 62:Question 1:Evaluate 11236. Answer:Using long division method:
∴ 11236=106 Page No 62:Question 2:Find the greatest number of five digits which is a perfect square. What is the square root of this number? Answer:The greatest 5 digit number is 99999. 316 < 99999 < 317 3162=99856 99856=316 Page No 62:Question 3:Find the least number of four digits which is a perfect square. What is the square root of this number? Answer:The least number of 4 digits is 1000.
31< 100< 32322= 1024 1024 is the least four digit perfect square and its square root is 32. Page No 62:Question 4:Evaluate 0.2809. Answer:∴ 0.2809=0.53 Page No 62:Question 5:Evaluate 3 correct up to two places of decimal. Answer:3=1.732Therefore, the value of 3 up to two places of decimal is 1.73. Page No 62:Question 6:Evaluate 48243 . Answer:48243=48243= 2×2×2×2×33×3×3×3×3=2×2×2×23×3×3×3=2×23×3=49 Page No 62:Question 7:Mark (✓) against the correct answer Answer:(d) 1222 A number ending in 2, 3, 7 or 8 is not a perfect square. Page No 62:Question 8:Mark (✓) against the correct answer Answer:(c) 112 2 14=94=94=3×32×2=32=112 Page No 62:Question 9:Mark (✓) against the
correct answer Answer:(c) 1764 The square of an even number is always even. Page No 62:Question 10:Mark (✓) against the correct answer Answer:Page No 62:Question 11:Mark (✓) against the correct answer Answer:Page No 62:Question 12:Mark (✓) against the correct answer Answer:(b) 84 72×98=2×2×2×3×3×2×7×7= 2×2×2×3×3×2×7×7=2×2×3×7=84 Page No 62:Question 13:Fill in the blanks. Answer:(i) 1+3 +5+7+9+11+13=(7)2 (ii) 1681=41 (iii) The smallest square number exactly divisible by 2, 4 and 6 is 36. LCM of 2,4 and 6 is12.Prime factorisation of 12 = 2× 2×3To make it a perfect square, we need to multiply it by 3.∴ 12×3 = 36 (iv) A given number is a perfect square having n digits, where n is odd. then, its square root will have n+12 digits. View NCERT Solutions for all chapters of Class 8 What is the perfect square of 6912?Therefore, we must divide by 3 to obtain a perfect square. 6912=2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3. It is a perfect square of 48.
What is the least number that can be multiplied to 6912 to make it a perfect cube?Answer: No 6912 is not a perfect cube. It should be multiplied by 2. Thus , it should be multiplied by 2 to make it a perfect cube.
What should be multiplied to 768 to make it a perfect square?So, 768 needs to be multiplied by 3 to become a perfect square.
IS 768 is a perfect square?Here the prime factor 3 is left without pairing, thus 768 is not a perfect square. The prime factors are all paired, thus we can say that 1296 is a perfect square.
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