Question

What is the square root of $1600$?

Answer 1

Determine the square root of $1600$.

The square root of a number is the value that returns the original number when multiplied by itself.

Find the prime factors of$1600$:

$1600=2\times 2\times 2\times 5\times 2\times 2\times 2\times 5$

Take square root from both sides of the above equation:

$$\begin{gathered} \sqrt{1600}=\sqrt{2\times 2\times 2\times 5\times 2\times 2\times 2\times 5} \\ \Rightarrow \sqrt{1600}=\sqrt{\underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{5\times 5}} \\ \Rightarrow \sqrt{1600}=2\times 2\times 2\times 5 \\ \Rightarrow \sqrt{1600}=40 \end{gathered}$$

Hence, the square root of $1600$ is $40$.