Question

Find the cube root of the number 91125.

Answer 1

Hint: In order to solve this problem you need to factorize 91125 in pairs of three by taking LCM. Then you will get the answer to this problem.

Complete step-by-step answer:
We need to find the cube root of 91125.
We know that 91125 can be written as :
91125 = 5 x 5 x 5 x 3 x 3 x 3 x 3 x 3 x 3
So, cube root of 91125 is
 $
  \sqrt[3]{{91125}} = \sqrt[3]{{5 \times 5 \times 5 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3}} = \sqrt[3]{{{5^3} \times {3^3} \times {3^3}}} \\
  \sqrt[3]{{91125}} = \sqrt[3]{{{5^3} \times {3^3} \times {3^3}}} = 5 \times 3 \times 3 = 45 \\
$
Hence the cube root of 91125 is 45.

Note: In this problem you have to factorize 91125 in pairs of 3 then you have to take cube root of it that is every term raised to the power $\dfrac{1}{3}$ then the pairs will be cancelled it will remove the cube root and you will get the cube root of 91125.