# How do you simplify (sqrt5)^2?

Sep 12, 2016

$\sqrt{{5}^{2}} = \sqrt{25} = 5 \text{ } {\left(\sqrt{5}\right)}^{2} = 5$

#### Explanation:

Adding and subtracting are inverse operations:

$15 \textcolor{b l u e}{+ 11} \textcolor{red}{- 11} = 15 \text{ } 15 \rightarrow 15$

Multiplication and division are inverse operations:

$23 \textcolor{b l u e}{\times 11} \textcolor{red}{\div 11} = 23 \text{ } 23 \rightarrow 23$

Square and square root are inverse operations:

$\textcolor{b l u e}{{\sqrt{17}}^{\textcolor{red}{2}}} = {\left(\textcolor{b l u e}{\sqrt{17}}\right)}^{\textcolor{red}{2}} = 17 \text{ } 17 \rightarrow 17$

$\sqrt{{x}^{2}} = {\left(\sqrt{x}\right)}^{2} = x \text{ } x \rightarrow x$

Inverse operations cancel each other out,

"One does, the other undoes."

The original number ends up the same.

$\sqrt{{5}^{2}} = \sqrt{25} = 5 \text{ " (sqrt5)^2 = 5" } 5 \rightarrow 5$