Question

Find the square root of $200$

Answer 1

Solve for the square root of given number

Given number is $200$

$\therefore$ prime factors of $200$ are

$$\begin{gathered} 200=2\times 100 \\ =2\times 2\times 50 \\ =2\times 2\times 2\times 25 \\ =2\times 2\times 2\times 5\times 5 \end{gathered}$$

$\therefore 200=2\times 2\times 2\times 5\times 5$

Taking Square root on both sides

$$\begin{gathered} \sqrt{200}=\sqrt{2\times 2\times 2\times 5\times 5} \\ =2\sqrt{25\times 4} \\ =10\sqrt{2} \\ =10\left(1.414\right) \\ =14.14 \end{gathered}$$

Hence, the square root of $200$ is $14.14$.