# What is the square root of 1/2?

Jun 1, 2018

See a solution process below:

#### Explanation:

Square root of $\frac{1}{2} = \sqrt{\frac{1}{2}}$

We can use this rule for radicals to rewrite the expression:

$\sqrt{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}} = \frac{\sqrt{\textcolor{red}{a}}}{\sqrt{\textcolor{b l u e}{b}}}$

$\sqrt{\frac{\textcolor{red}{1}}{\textcolor{b l u e}{2}}} \implies \frac{\sqrt{\textcolor{red}{1}}}{\sqrt{\textcolor{b l u e}{2}}} \implies \frac{1}{\sqrt{2}}$

Now, we can rationalize the denominator, or, in other words, remove the radical from the denominator, by multiplying by the appropriate form of $1$:

$\frac{\sqrt{2}}{\sqrt{2}} \times \frac{1}{\sqrt{2}} \implies$

$\frac{\sqrt{2} \times 1}{\sqrt{2} \times \sqrt{2}} \implies$

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

$\frac{\sqrt{2}}{2}$

If, a decimal number is needed:

$\frac{\sqrt{2}}{2} \cong \frac{1.4142}{2} \cong 0.7071$