How do you simplify sqrt12 / sqrt5?

Jul 15, 2017

See a solution process below:

Explanation:

First, we can rationalize the denominator by multiplying the the fraction by the appropriate form of $1$:

$\frac{\sqrt{5}}{\sqrt{5}} \cdot \frac{\sqrt{12}}{\sqrt{5}} \implies$

$\frac{\sqrt{5} \cdot \sqrt{12}}{\sqrt{5} \cdot \sqrt{5}} \implies$

$\frac{\sqrt{5 \cdot 12}}{5} \implies$

$\frac{\sqrt{60}}{5}$

Next, we can simplify the numerator as follows:

$\frac{\sqrt{60}}{5} \implies$

$\frac{\sqrt{4 \cdot 15}}{5} \implies$

$\frac{\sqrt{4} \cdot \sqrt{15}}{5} \implies$

$\frac{2 \sqrt{15}}{5}$

Jul 15, 2017

$\frac{2 \sqrt{15}}{5}$

Explanation:

First, multiply the numerator and denominator by $\sqrt{5}$, which will get rid of the radical in the denominator. This is essentially the same as multiplying the expression by $1$.

$\frac{\sqrt{12}}{\sqrt{5}} \cdot \textcolor{b l u e}{\frac{\sqrt{5}}{\sqrt{5}}}$

$\sqrt{5} \cdot \sqrt{5} = \sqrt{25} = 5$, so the denominator becomes $5$. Similarly, $\sqrt{12} \cdot \sqrt{5} = \sqrt{60}$.

$= \frac{\sqrt{60}}{5}$

Now, we can split $\sqrt{60}$ into $\sqrt{4} \cdot \sqrt{15}$.

$= \frac{\sqrt{4} \cdot \sqrt{15}}{5}$

$= \frac{2 \sqrt{15}}{5}$