Question

Find the least number of which 65856 should be divided to make it a perfect cube . Also find the cube root of the perfect cube .
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Answer 1

$\huge\bold{\textbf{\textsf{{\color{cyan}{Answer}}}}}$

3

Answer 2

To Find :- The least number of which 65856 should be divided to make it a perfect cube . Also find the cube root of the perfect cube . ?

Solution :-

Finding prime factors of 65856 we get,

→ 65856 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 7 * 7 * 7

→ 65856 = (2 * 2 * 2) * (2 * 2 * 2) * 3 * (7 * 7 * 7)

now, we know that, for a number to be a perfect cube number its all prime must be in pair of three .

But as we can see that, prime factors of 65856 have one prime factor as 3 only . So, if we divide the number by 3 it will be cancel and remaining prime factors will be in pair of 3 .

Therefore, we can conclude that, the least number of which 65856 should be divided to make it a perfect cube is equal to 3 .

and then, the cube root of number so formed will be,

→ 65856 ÷ 3 = {(2 * 2 * 2) * (2 * 2 * 2) * 3 * (7 * 7 * 7)} ÷ 3

→ 21952 = (2 * 2 * 2) * (2 * 2 * 2) * (7 * 7 * 7)

hence,

→ Required cube root = 2 * 2 * 7 = 28 (Ans.)

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