Question

Find the cube root of the number – 17576 using the factorization method.

Answer 1

Hint: To find the cube root of the number we factorize the given number until we get a number which is raised to the power of 3.

Complete step-by-step answer:
Let us first find the cube root of 17576, i.e. $\sqrt[3]{{ 17576}}$
We express the number 17576 as a product of prime numbers.

We have,
17576 =2 × (8788)
             =2 × 2 × (4394)
             =2 × 2 × 2 × (2197)
             =2 × 2 × 2 × 13 × (169)
             =2 × 2 × 2 × 13 × 13 × 13
             = (2 × 13) × (2 × 13) × (2 × 13)
             = 26 × 26 × 26.

This shows that −17567 = (−26) × (−26) × (−26).
Thus −17576 ​ =${\left( { - 26} \right)^3}$.

The cube root of – 17567, i.e. -$\sqrt[3]{{ 17576}}$= -26.


Note: In order to solve such types of problems the key is to express the given number as a product of prime numbers, then we rewrite all its factors until we achieve a number raised to the power 3 as we are supposed to find the cube root.
We apply the same procedure to find the square root, fourth root, fifth root and so on of a number, we write down all the factors of the number and try to express them as a number raised to the power of 4 for fourth root, power 5 for the fifth root and so on.