Chapter 8.2, Problem 10CE

To determine

To Simplify: Simplify the given expression

Answer to Problem 10CE

The simplified form is ${\left(\frac{\sqrt{2}}{2}\right)}^2=\frac{1}{2}$

Explanation of Solution

Given information: The given expression is ${\left(\frac{\sqrt{2}}{2}\right)}^2$

We have the given expression is ${\left(\frac{\sqrt{2}}{2}\right)}^2$

It can be further written as

  $\begin{array}{c}{\left(\frac{\sqrt{2}}{2}\right)}^2=\left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{2}}{2}\right)\\ =\left(\frac{\sqrt{2}.\sqrt{2}}{2^2}\right)\\ =\left(\frac{\sqrt{2^2}}{2^2}\right)\\ =\left(\frac{2}{4}\right)\\ =\frac{1}{2}\end{array}$

Since square root is positive quantity so we neglect negative sign.

Therefore, the simplified form is ${\left(\frac{\sqrt{2}}{2}\right)}^2=\frac{1}{2}$