# NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.1 Part 2 (For CBSE, ICSE, IAS, NET, NRA 2023)

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

(i) 243

(ii) 256

(iii) 72

(iv) 675

(v) 100

(i) 243

 3 243 3 81 3 27 3 9 3 3 1

Prime factors of

To make 243 a cube, one more 3 is required.

Hence, the number 243 multiply by 3 to obtain a perfect cube.

(ii) 256

 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1

Prime factors of 256 =

To make 256 a cube, one more 2 is required.

Hence, the number 256 multiply by 2 to obtain a perfect cube.

(iii) 72

 2 72 2 36 2 18 3 9 3 3 1

Prime factors of

To make 72 a cube, one more 3 is required.

Hence, the number 72 multiply by 3 to obtain a perfect cube.

(iv) 675

 3 675 3 225 3 75 5 25 5 5 1

Prime factors of

To make 675 a cube, one more 5 is required.

Hence, the number 675 multiply by 5 to obtain a perfect cube.

(v) 100

 2 100 2 50 5 25 5 5 1

Prime factors of

To make 100 a cube, we require one more 2 and one more 5.

Hence, the number 100 multiply by to obtain a perfect cube.