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Cubes and Cube Roots

Short Answer Type

11.
Is 216 a perfect cube? What is the number whose cube is 216?

We have 216
We have 216i.e. Resolving 216 into prime factors we have: 216 = 2 x 2

i.e. Resolving 216 into prime factors we have: 216 = 2 x 2 x 2 x 3x 3 x 3

i.e. 216 can be resolved in to such prime factor which can be grouped into triple of equal of factor and no factor is left over.

∴ 216 is a perfect cube
We have 216i.e. Resolving 216 into prime factors we have: 216 = 2 x 2
Thus, the required number is 6, whose cube is 216.

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Long Answer Type

12.

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704

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Short Answer Type

13. 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?

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14.

Find the cube root of 1728.

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15.

Fint the cube root of 27000 by prime factorisation.

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16. State true or false: for any integer m, m² < m³. Why?

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17. What is the smallest number by which 288 must be multiplied so that the product is a perfect cube?

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18.

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