Question

Solve each equation. Check your solution.

$\sqrt{a-2}=6$

Short answer

The solution of the given equation is $a=38$.

Check:

Substitute 38 for a in the given equation $\sqrt{a-2}=6$.

$$\begin{gathered} \sqrt{a-2}=6 \\ \sqrt{38-2}\underset{¯}{\underset{¯}{?}}6 \\ \sqrt{36}\underset{¯}{\underset{¯}{?}}6 \\ \text{6}=6 \end{gathered}$$

Therefore,$a=38$is the solution of the given equation $\sqrt{a-2}=6$.

Step-by-step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$$\begin{gathered} \sqrt{a-2}=6 \\ {\left(\sqrt{a-2}\right)}^2=6^2\left(\text{squaringbothsides}\right) \\ a-2=36 \end{gathered}$$

Step 2. Solve the given equation.

The solution of the given equation is:

$$\begin{gathered} a-2=36 \\ a=36+2 \\ a=38 \end{gathered}$$

Therefore, the solution of the given equation is $a=38$.

Step 3. Check the solution.

Substitute 38 for in the given equation $\sqrt{a-2}=6$.

$$\begin{gathered} \sqrt{a-2}=6 \\ \sqrt{38-2}\underset{¯}{\underset{¯}{?}}6 \\ \sqrt{36}\underset{¯}{\underset{¯}{?}}6 \\ \text{6}=6 \end{gathered}$$

Therefore,$a=38$ is the solution of the given equation $\sqrt{a-2}=6$.