Question

Which one is the correct square root of $800$.

• A. $2\sqrt{20}$
• B. $20\sqrt{2}$
• C. $40\sqrt{2}$
• D. none of these

Answer 1

The correct option is B

$20\sqrt{2}$

To find the square root of $800$, we will express it in terms of its prime factors using prime factorization:

It can be written as $$\begin{gathered} 800=2\times 2\times 2\times 2\times 2\times 5\times 5 \\ 800=2^5\times 5^5 \end{gathered}$$

Taking root on both sides:

$$\begin{gathered} \sqrt{800}=\sqrt{\left(2^5\times 5^5\right)} \\ \sqrt{800}=5\times 2^2\times \sqrt{2} \\ \sqrt{800}=20\sqrt{2} \end{gathered}$$

Hence, option B is the correct answer.