Question

find the cube root of_15625​

Answer 1

Question

Find the cube root of 15625.

Answer

The cube root of 15625 is 25.

By prime factorization method:

15625 = 5 × 5 × 5 × 5 ×5 × 5

15625 = (5×5×5)(5×5×5)

= 5 × 5

= 25

Hence, verified!

By estimation method

We will make groups of three digits starting from the digit of the number 15625. Groups are 15 and 625.

Considering the group 625,it ends with 5. We know that if the digit 5 is at the end of a perfect cube number its cube root will have its unit place digit as 5 only.

Therefore, the unit place digit of the required cube root can be taken as 5.

Taking the other group that is 15, We know that, 2³=8 and 3³=27. 8< 15 < 27. 2 is smaller between 2 and 3.

Therefore, 2 will be taken at the tens place of required cube root.

Therefore ³√15625 = 25

Hence, verified!

Answer 2

$by \: prime \: factorization \: method \\ \\ 15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = {5}^{6} \\ \\ \sqrt[3]{15625} = ( {5}^{6)\frac{1}{3} } = {5}^{2 } = 25$