Chapter 8.1, Problem 15WE

To determine

The given expression

Answer to Problem 15WE

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

Explanation of Solution

Given information:

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

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

It can be further written as

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

Since square root is positive quantity so neglecting negative sign.

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