# How do you simplify sqrt(0.25)?

May 15, 2016

$\sqrt{0.25} = \pm 0.5$

#### Explanation:

consider $\text{ } 5 \times 5 = 25$

Note that $0.5 \to \frac{5}{10} \to 5 \times \frac{1}{10}$

$\left(\textcolor{red}{5} \times \textcolor{g r e e n}{\frac{1}{10}}\right) \times \left(\textcolor{red}{5} \times \textcolor{g r e e n}{\frac{1}{10}}\right) = \textcolor{red}{25} \times \textcolor{g r e e n}{\frac{1}{100}} = 0.25$

so $\sqrt{0.25} = \sqrt{\left(5 \times \frac{1}{10}\right) \times \left(5 \times \frac{1}{10}\right)} = 5 \times \frac{1}{10} = 0.5$

so $\sqrt{0.25} = \pm 0.5$

Oct 18, 2017

A better way of solving this

#### Explanation:

Note that $0.25$ is the same as $25 \times \frac{1}{100}$

Thus $\sqrt{0.25} \textcolor{w h i t e}{\text{dd")=color(white)("dd")sqrt(25xx1/100)color(white)("dd") =color(white)("dd}} \frac{\sqrt{25}}{\sqrt{100}}$

$\pm \frac{5}{10} = \pm 0.5$