Class 8 Maths

# Cube and Cube Root

## Exercise 7.1

Question 1: Which of the following numbers are not perfect cubes?

(i) 216

Answer: 216 = 2 xx 2 xx 2 xx 27
= 2 xx 2 xx 2 xx 3 xx 3 xx 3

3sqrt(216)=2xx3=6

As number of 2s and 3s is 3 in the factorization so it is a perfect cube.

(ii) 128

Answer: 128 = 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2
Number of 2s is 7 and 7 is not divisible by three so 128 is not a perfect cube

(iii) 1000

Answer: 1000 = 2 xx 2 xx 2 xx 5 xx 5 xx 5
Number of 2s and 5s is 3 each so 1000 is a perfect cube.

(iv) 100

Answer: 100 = 2 xx 2 xx 5 xx 5
Number of 2s and 5s is 2 each and not 3 so 100 is not a perfect cube.

(v) 46656

Answer: 46656 = 2 xx 2 xx 2 xx 5832
= 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 729
= 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 3 xx 3 xx 3 xx 3
Number of 2s and 3s is 6 each and 6 is divisible by 3 so 46656 is a perfect cube

Question 2: Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243

Answer: 243 = 3 xx 3 xx 3 xx 3 xx 3
Number of 3s is 5, so we need to another 3 in the factorization to make 243 a perfect cube. 243 multiplied by 3 will be a perfect cube.

(ii) 256

Answer: 256 = 2 x 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2
Number of 2s is 8 so 256 needs to be multiplied by 2 to become a perfect cube.

(iii) 72

Answer: 72 = 2 xx 2 xx 2 xx 3 xx 3
Number of 2s is 3 and that of 3s is 2, so 72 needs to be multiplied by 3 to become a perfect cube.

(iv) 675

Answer: 675 = 5 xx 5 xx 27 = 5 xx 5 xx 3 xx 3 xx 3
675 needs to be multiplied by 5 to become a perfect cube.

(v) 100

Answer: 100 = 10 x 10
100 needs to be multiplied by 10 to become a perfect cube.

Question 3: Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.

(i) 81

Answer: 81 = 3 xx 3 xx 3 xx 3
81 needs to be divided by 3 to become a perfect cube.

(ii) 128

Answer: 128 = 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2
128 needs to be divided by 2 to become a perfect cube.

(iii) 135

Answer: 135 = 5 xx 3 xx 3 xx 3
135 needs to be divide by 5 to become a perfect cube.

(iv) 192

Answer: 192 = 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 3
192 needs to be divided by 3 to become a perfect cube.

(v) 704

Answer: 704 = 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 11
704 needs to be divided by 11 to become a perfect cube.

Question 4: Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

Answer: To find the answer we need to calculate the LCM of 5 and 2. The cube with each sides measuring equal to the LCM will give the dimensions of required cube.
LCM of 5 and 2 = 10
Volume of cuboid = 5 xx 5 xx 2=50 cubic cms
Volume of bigger cube =10^3=1000 cubic cms
Number of cuboids required to make the bigger cube

=text(Volume of bigger cube)/text(Volume of cuboid)

=(1000)/(50)=20

Ex 7.1

Ex 7.2