Chapter 9.3, Problem 32P

Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth. $5a^2-\frac{1}{125}=0$

To determine

To Find:

The number of solutions of the given equation.

Answer to Problem 32P

The given equation has two solutions $a=\frac{1}{25},a=-\frac{1}{25}$ .

Explanation of Solution

Given information:

The given equation is $5a^2-\frac{1}{125}=0$ .

Consider the given equation $5a^2-\frac{1}{125}=0$ .

  $5a^2-\frac{1}{125}=0$

Add $\frac{1}{125}$ from both sides.

  $\begin{array}{l}5a^2-\frac{1}{125}+\frac{1}{125}=0+\frac{1}{125}\\ 5a^2=\frac{1}{125}\\ a^2=\frac{1}{625}\\ a=\frac{1}{25},a=-\frac{1}{25}\end{array}$

Therefore, the given equation has two solutions $a=\frac{1}{25},a=-\frac{1}{25}$ .