# How do you simplify sqrt5 div sqrt3?

$\frac{\sqrt{15}}{3}$
$\sqrt{5} \div \sqrt{3}$ can be rewritten as $\frac{\sqrt{5}}{\sqrt{3}}$.
As there is a surd (radical) on the botoom, we have to rationalise the denominator, to do this we use the equation: $\frac{a}{\sqrt{b}} \equiv \frac{a \cdot \sqrt{b}}{{\sqrt{b}}^{2}} = \frac{a \sqrt{b}}{b}$.
In this case, $a = \sqrt{5}$ and $b = \sqrt{3}$. By putting our values in we get: $\frac{\sqrt{5}}{\sqrt{3}} \equiv \frac{\sqrt{5} \cdot \sqrt{3}}{{\sqrt{3}}^{2}} = \frac{\sqrt{5 \cdot 3}}{3} = \frac{\sqrt{15}}{3}$. As none of the factors of 15 are perfect squares, this fraction cannot be simplified.