Question

Simplify each expression.

${\left(\frac{\sqrt{2}}{2}\right)}^2$

Short answer

The simplified form is,

${\left(\frac{\sqrt{2}}{2}\right)}^2=\frac{1}{2}$.

Step-by-step solution

Step 1. Given information.

The given expression is,

${\left(\frac{\sqrt{2}}{2}\right)}^2$.

Step 2. It can be further written as below.

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

Then,

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

Step 3. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

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