How do you rationalize the denominator and simplify 8/sqrt2?

Aug 12, 2016

$4 \sqrt{2}$

Explanation:

$\textcolor{b l u e}{\text{Rationalising}}$ the denominator means 'removing' the radical from the denominator and leaving a rational value in it's place.

To do this we make use of the following fact.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\sqrt{a} \times \sqrt{a} = a} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \sqrt{2} \times \sqrt{2} = 2 \text{ a rational number}$

Since this is a fraction we must also multiply the numerator by $\sqrt{2}$

$\Rightarrow \frac{8}{\sqrt{2}} = \frac{8}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$= \frac{8 \sqrt{2}}{2} = \frac{{\cancel{8}}^{4} \sqrt{2}}{\cancel{2}} ^ 1 = 4 \sqrt{2} \text{ in simplest form}$