Question

Find the square root of $6400$.

Answer 1

Solve for the square root of given number:

Given number is $6400$

By using the Prime factorization method, we get,

$$\begin{gathered} 6400=2\times 3200 \\ =2\times 2\times 1600 \\ =2\times 2\times 2\times 800 \\ =2\times 2\times 2\times 2\times 400 \\ =2\times 2\times 2\times 2\times 2\times 200 \\ =2\times 2\times 2\times 2\times 2\times 2\times 100 \\ =2\times 2\times 2\times 2\times 2\times 2\times 2\times 50 \\ =2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 25 \\ =2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5\times 5 \end{gathered}$$

$\therefore 6400=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5\times 5$

Applying square root on both sides,

$\Rightarrow \sqrt{6400}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5\times 5}$

$=2\times 2\times 2\times 2\times 5$

$=80$

Hence, the square root of $6400$ is $80$.