Chapter 12.1, Problem 12WE

To determine

To solve: The equation $7m^2-42=0$ and express irrational solution in simplest radical form.

Answer to Problem 12WE

The solution set is $\left(\sqrt{6},-\sqrt{6}\right)$ .

Explanation of Solution

Given information:

The given equation $7m^2-42=0$ .

Calculation:

  $\begin{array}{l}\Rightarrow 7m^2-42=0\\ \Rightarrow 7m^2-42+42=0+42\end{array}$

(Adding 42 on both sides)

  $\begin{array}{l}\Rightarrow 7m^2=42\\ \Rightarrow \frac{7m^2}{7}=\frac{42}{7}\end{array}$

(Divide by 7 on both sides)

  $\begin{array}{l}\Rightarrow m^2=6\\ \Rightarrow m=\pm \sqrt{6}\end{array}$

Therefore, the solution set is $\left(\sqrt{6},-\sqrt{6}\right)$ .