# NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.1 Part-3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question: 3 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

(i) 81

 3 81 3 27 3 9 3 3 1

Prime Factors of

Here, one 3 is left which is not in a triplet.

If we divide 81 by 3, then it will become a perfect cube.

Thus, is a perfect cube.

Hence, 81 divided by 3 to make it a perfect cube.

(ii) 128

 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1

Prime Factors of

Here, one 2is left which is not in a triplet.

If we divide by 2, then it will become a perfect cube.

Thus, is a perfect cube.

Hence, 128 divided by 2 to make it a perfect cube.

(iii) 135

 3 135 3 45 3 15 5 5 1

Prime Factors of

Here, one 2 is left which is not in a triplet.

If we divide 135 by 5, then it will become a perfect cube

Thus, is a perfect cube.

Hence, 135 divided by 5 to make it a perfect cube.

(iv) 192

 2 192 2 96 2 48 2 24 2 12 2 6 3 3 1

Prime Factors of

Here, one 3 is left which is not in a triplet.

If we divide 192 by 3, then it will become a perfect cube

Thus, is a perfect cube.

Hence, 192 divided by 3 to make it 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?