Question

Find the cube root of 512.

Answer 1

Hint:
According to the given question, we will start making factors of 512. That means we will start with the smallest prime number of 512 till the quotient becomes 1. Hence, take all the factors from which number you are dividing and make all the triplet pairs to get the cube root.

Complete step by step solution:
As, we have to calculate the cube root of 512 by factorization method.
Here, we will start dividing the number with the smallest prime number that is 2 till it leaves quotient 1.
So, we will start with the given value that is 512.
512 = \[\dfrac{{512}}{2}\]
On dividing with 2 we get = 256
Here, again we will continue dividing the quotient that is 256.
256 = \[\dfrac{{256}}{2}\]
On dividing with 2 we get = 128

Here, again we will continue dividing the quotient that is 128.
128 = \[\dfrac{{128}}{2}\]
On dividing with 2 we get = 64
Here, again we will continue dividing the quotient that is 64.
64 = \[\dfrac{{64}}{2}\]
On dividing with 2 we get = 32
Here, again we will continue dividing the quotient that is 32.
32 = \[\dfrac{{32}}{2}\]
On dividing with 2 we get = 16
Here, again we will continue dividing the quotient that is 16.
16 = \[\dfrac{{16}}{2}\]
On dividing with 2 we get = 8
Here, again we will continue dividing the quotient that is 8.
8 = \[\dfrac{8}{2}\]
On dividing with 2 we get = 4
Here, again we will continue dividing the quotient that is 4.
4 = \[\dfrac{4}{2}\]
On dividing with 2 we get = 2
Here, again we will continue dividing the quotient that is 2.
2 = \[\dfrac{2}{2}\]
On dividing with 2 we get = 1.
Therefore, Calculated Prime Factors of 256 are
\[512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\;\]
Taking out one prime number from the triplet of prime numbers from the above equation. We get:
\[256 = 2 \times 2 \times 2\]

Hence, \[\sqrt[3]{{512}} = 8\]

Note:
To solve these types of questions, we must remember to find all the factors of the given number in the prime number. Similarly we can find out the square root of the given number by just taking out pairs of the prime number from the calculated factors.