What is the smallest number by which 12348 may be multiplied so that the product is a perfect cube?

Question 10 Cube and Cube Roots Exercise 4.1

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Answer:

(i) 675

First find the factors of 675

675 = 3 × 3 × 3 × 5 × 5

= 33 × 52

∴To make a perfect cube we need to multiply the product by 5.

(ii) 1323

First find the factors of 1323

1323 = 3 × 3 × 3 × 7 × 7

= 33 × 72

∴To make a perfect cube we need to multiply the product by 7.

(iii) 2560

First find the factors of 2560

2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

= 23 × 23 × 23 × 5

∴To make a perfect cube we need to multiply the product by 5 × 5 = 25.

(iv) 7803

First find the factors of 7803 7803 = 3 × 3 × 3 × 17 × 17

= 33 × 172

∴To make a perfect cube we need to multiply the product by 17.

(v) 107811

First find the factors of 107811 107811 = 3 × 3 × 3 × 3 × 11 × 11 × 11

= 33 × 3 × 113

∴To make a perfect cube we need to multiply the product by 3 × 3 = 9.

(vi) 35721

First find the factors of 35721

35721 = 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7

= 33 × 33 × 72

∴To make a perfect cube we need to multiply the product by 7.

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