Question

Find the length of side x in simplest radical form with a rational denominator

Answer 1

It's the triangle 30° - 60° - 90°.

The sides are in proportion 1 : √3 : 2 (look at the picture).

Therefore we have:

$x=\dfrac{\sqrt6\cdot\sqrt3}{2}=\dfrac{\sqrt{(6)(3)}}{2}=\dfrac{\sqrt{18}}{2}=\dfrac{\sqrt{(9)(2)}}{2}\\\\=\dfrac{\sqrt9\cdot\sqrt2}{2}=\boxed{\dfrac{3\sqrt2}{2}}$