Question

find the cube root of the following without factorization 17576​

Answer 1

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Answer 2

Answer:

The cube root of – 17567, i.e. -17576√3= -26.

Step-by-step explanation:

Let us first find the cube root of 17576, i.e. 17576−−−−−√3

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 ​ =(−26)3.

The cube root of – 17567, i.e. -17576−−−−−√3= -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.