# What is the square root of 700?

May 26, 2018

$10 \sqrt{7} \leftarrow \text{ Exact answer}$

$26.457513 \ldots \to 26.46$ Approximate answer to 2 decimal places

#### Explanation:

Before we start note that 7 is a prime number.

You need to look for squared values that you can 'take outside' the root.

Write 700 as $7 \times 100$

Not that 100 is the same as $4 \times 25 \to {2}^{2} \times {5}^{2}$ giving:

$\sqrt{700} = \sqrt{7 \times {2}^{2} \times {5}^{2}}$

$\textcolor{w h i t e}{\text{dddddddd}} 2 \times 5 \times \sqrt{7}$

color(white)("dddddddd")10sqrt(7) larr" Exact answer"