Question

Find the square root of $784$.

Answer 1

Solve for the square root of given number:

Given number is $784$

By using the Prime factorization method, we get,

$$\begin{gathered} 784=2\times 392 \\ =2\times 2\times 196 \\ =2\times 2\times 2\times 98 \\ =2\times 2\times 2\times 2\times 49 \\ =2\times 2\times 2\times 2\times 7\times 7 \end{gathered}$$

$\therefore 784=2\times 2\times 2\times 2\times 7\times 7$

Applying square root on both sides,

$\sqrt{784}=\sqrt{2\times 2\times 2\times 2\times 7\times 7}$

$=2\times 2\times 7$

$=28$

$\therefore \sqrt{784}=28$

Hence, the square root of $784$ is $28$.