# Cube And Cube Roots

Exercise 1

1. Which of the following numbers are not perfect cubes?

(i) 216

Answer: 216 = 2 x 2 x 2 x 27

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

(ii) 128

Answer: 128 = 2 x 2 x 2 x 2 x 2 x 2 x 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 x 2 x 2 x 5 x 5 x 5

Number of 2s and 5s is 3 each so 1000 is a perfect cube.

(iv) 100

Answer: 100 = 2 x 2 x 5 x 5

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

(v) 46656

Answer: 46656 = 2 x 2 x 2 x 5832

= 2 x 2 x 2 x 2 x 2 x 2 x 729

= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

Number of 2s and 3s is 6 each and 6 is divisible by 3 so 46656 is a perfect cube

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 x 3 x 3 x 3 x 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 x 2 x 2 x 2 x 2 x 2 x 2

Number of 2s is 8 so 256 needs to be multiplied by 2 to become a perfect cube.

(iii) 72

Answer: 72 = 2 x 2 x 2 x 3 x 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 x 5 x 27 = 5 x 5 x 3 x 3 x 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.

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 x 3 x 3 x 3

81 needs to be divided by 3 to become a perfect cube.

(ii) 128

Answer: 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

128 needs to be divided by 2 to become a perfect cube.

(iii) 135

Answer: 135 = 5 x 3 x 3 x 3

135 needs to be divide by 5 to become a perfect cube.

(iv) 192

Answer: 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

192 needs to be divided by 3 to become a perfect cube.

(v) 704

Answer: 704 = 2 x 2 x 2 x 2 x 2 x 2 x 11

704 needs to be divided by 11 to become a perfect cube.

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 x 5 x 2 cubic cms

Volume of bigger cube=103=1000 cubic cms

Number of cuboids required to make the bigger cube =  Cube And Cube Roots will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.