Question

By which least number should 972 be divided so that it is a perfect cube?
Find the perfect cube number. Also, find the cube root​

Answer 1

Here you go....

first do prime factorization of 972..

it will give you factors

2×2×3×3×3×3×3

Now u have to divide it such that it will be a perfect cube

2×2×3×3×3×3×3/2×2×3×3

hence u need to divide 972 by 36 which will give u 27

27 is cube of 3

3 is cube root of 27

Hope it helps...

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Answer 2

Answer:

6

Step-by-step explanation:

$\sqrt[3]{972} = \sqrt[3]{2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3}$

$= 3 \sqrt[3]{ {2}^{2} \times {3}^{2} }$

hence, 972 should be multiplied by 2×3=6 for it to become a perfect cube

The perfect cube number:

972×6=5832

$\sqrt[3]{5832} = \sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3}$

$= 2 \times 3 \times 3 \ \\ = 18$