which is the best way to find square roots and cube roots of long and big numbers - Maths - Heron\s Formula

Question

which is the best way to find square roots and cube roots of
long and big numbers??

Harleen Birdi · Accepted Answer

The simplest method of finding the square root, cube root of any bigger number is to make the factors of that number.

Square root:

For example, take a number 4225 and factorize it.

$\begin{matrix} 5 & 4225 \\ 5 & 845 \\ 13 & 169 \\ 13 & 13 \\ 1 \end{matrix}$

∴ Factors of 4225 = 5 × 5 × 13 × 13

Now there are two pairs viz 5 × 5 and 13 × 13

So on taking square root of 4225, we have

$\sqrt{4225} = \sqrt{5 \times 5 \times 13 \times 13} = 5 \times 13 = 65$

So, the square root of 4225 is 65.

Cube root

For example, take a number 5832 and factorize it.

$\begin{matrix} 2 & 5832 \\ 2 & 2916 \\ 2 & 1458 \\ 3 & 729 \\ 3 & 245 \\ 3 & 81 \\ 3 & 27 \\ 3 & 9 \\ 3 & 3 \\ 1 \end{matrix}$

∴ Factors of 5832 is 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Now, make the triplet as follows:

$\underset{̲}{2 \times 2 \times 2} \underset{̲}{\times 3 \times 3 \times 3} \underset{̲}{\times 3 \times 3 \times 3}$

On taking cube roots of 5832, we have

$\sqrt[3]{5832} = \sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3}$

= 2 × 3 × 3 = 18

So, 5832 is a cube root of 18.

which is the best way to find square roots and cube roots of long and big numbers??