# How do you rationalize the denominator and simplify sqrt(3/2)?

May 5, 2018

I got as far as this:

#### Explanation:

Let us write it as:

$\frac{\sqrt{3}}{\sqrt{2}}$

multiply and divide by $\sqrt{2}$

$\frac{\sqrt{3}}{\sqrt{2}} \textcolor{red}{\frac{\sqrt{2}}{\sqrt{2}}} = \frac{\sqrt{3} \sqrt{2}}{2} = = \frac{\sqrt{3 \cdot 2}}{2} = \frac{\sqrt{6}}{2}$

May 5, 2018

$\frac{\sqrt{6}}{2}$

#### Explanation:

$\sqrt{\frac{3}{2}}$

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

$\therefore = \frac{\sqrt{3}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$\therefore = \sqrt{2} \times \sqrt{2} = 2$

$\therefore = \frac{\sqrt{2 \times 3}}{2}$

$\therefore = \frac{\sqrt{6}}{2}$

May 5, 2018

$\frac{\sqrt{6}}{2} = \frac{1}{2} \sqrt{6}$

#### Explanation:

$\text{using the "color(blue)"laws of radicals}$

•color(white)(x)sqrt(a/b)hArrsqrta/sqrtb

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)

•color(white)(x)sqrtaxxsqrta=a

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

$\text{to eliminate the radical on the denominator multiply}$
$\text{the numerator/denominator by } \sqrt{2}$

$\Rightarrow \frac{\sqrt{3}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{3} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{\sqrt{6}}{2} = \frac{1}{2} \sqrt{6}$