# How do you simplify root3(3/4)?

Apr 23, 2017

$\sqrt{\frac{3}{4}} = \frac{\sqrt{6}}{2}$

#### Explanation:

For any non-zero values of $a , b$ we have:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$\sqrt{{a}^{3}} = a$

So we find:

$\sqrt{\frac{3}{4}} = \sqrt{\frac{3 \cdot 2}{4 \cdot 2}} = \sqrt{\frac{6}{2} ^ 3} = \frac{\sqrt{6}}{\sqrt{{2}^{3}}} = \frac{\sqrt{6}}{2}$

Notice how making the denominator into a perfect cube before splitting the radical allows us to avoid having to rationalise the denominator afterwards.

Apr 23, 2017

color(blue)(root3(6)/2

#### Explanation:

$\sqrt{\frac{3}{4}}$

$\therefore = \frac{\sqrt{3}}{\sqrt{4}} \times \frac{\sqrt{4}}{\sqrt{4}} \times \frac{\sqrt{4}}{\sqrt{4}}$

:.=color(blue)(root3(4)*root3(4)*root3(4)=4

$\therefore = \frac{\sqrt{48}}{4}$

$\therefore = \frac{\sqrt{3 \cdot 2 \cdot 2 \cdot 2 \cdot 2}}{4}$

$\therefore = \frac{{\cancel{2}}^{\textcolor{b l u e}{1}} \sqrt{6}}{\cancel{4}} ^ \textcolor{b l u e}{2}$

:.=color(blue)(root3(6)/2