Chapter A.1, Problem 38E

Solution

Rationalize the denominator.

  $\frac{\sqrt{5}}{5}$ .

Given:

The given expression is $\frac{1}{\sqrt{5}}$ .

Concept Used:

• Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
• Make sure all radicals are simplified.
• Simplify the fraction if needed.

Calculation:

The given expression is $\frac{1}{\sqrt{5}}$ .

Multiply the given expression $\frac{1}{\sqrt{5}}$ both numerator and denominator by $\sqrt{5}$ .

  $\begin{array}{c}\frac{1}{\sqrt{5}}=\frac{1}{\sqrt{5}}\cdot \frac{\sqrt{5}}{\sqrt{5}}\\ =\frac{\sqrt{5}}{5}\end{array}$

Thus after rationalize the given expression $\frac{1}{\sqrt{5}}$ is $\frac{\sqrt{5}}{5}$ .