Question

Simplify.

$\frac{\sqrt{15}}{3\sqrt{45}}$

Short answer

The simplified form is $\frac{\sqrt{15}}{3\sqrt{45}}=\frac{\sqrt{3}}{9}$.

Step-by-step solution

Step 1. Given information.

The given expression is $\frac{\sqrt{15}}{3\sqrt{45}}$

Step 2. It can be further written as below.

The given expression is $\frac{\sqrt{15}}{3\sqrt{45}}$

Then,

$\begin{array}{c}\frac{\sqrt{15}}{3\sqrt{45}}=\frac{\sqrt{15}}{3\sqrt{3^2\times 5}}\\ =\frac{\sqrt{15}}{3\times 3\sqrt{5}}\\ =\frac{\sqrt{3\times 5}}{9\sqrt{5}}\\ =\frac{\sqrt{3}\times \sqrt{5}}{9\sqrt{5}}\\ =\frac{\sqrt{3}}{9}\end{array}$

Step 3. Neglect negative sign.

Since, square root is positive quantity.

Therefore, the simplified form is $\frac{\sqrt{15}}{3\sqrt{45}}=\frac{\sqrt{3}}{9}$.