Question

Solve each equation. Check your solution.

$\sqrt{a+4}=6$

Short answer

The solution of the given equation is $a=32$.

Check:

Substitute 32 for a in the given equation $\sqrt{a+4}=6$.

$$\begin{gathered} \sqrt{a+4}=6 \\ \sqrt{32+4}\underset{¯}{\underset{¯}{?}}6 \\ \sqrt{36}\underset{¯}{\underset{¯}{?}}6 \\ \text{6}=6 \end{gathered}$$

Therefore,$a=32$ is the solution of the given equation $\sqrt{a+4}=6$.

Step-by-step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$$\begin{gathered} \sqrt{a+4}=6 \\ {\left(\sqrt{a+4}\right)}^2=6^2\left(\text{squaringbothsides}\right) \\ a+4=36 \end{gathered}$$

Step 2. Solve the given equation.

The solution of the given equation is:

$$\begin{gathered} a+4=36 \\ a=36-4 \\ a=32 \end{gathered}$$

Therefore, the value a is 32.

Step 3. Check the solution.

Substitute 32 for a in the given equation $\sqrt{a+4}=6$.

$$\begin{gathered} \sqrt{a+4}=6 \\ \sqrt{32+4}\underset{¯}{\underset{¯}{?}}6 \\ \sqrt{36}\underset{¯}{\underset{¯}{?}}6 \\ \text{6}=6 \end{gathered}$$

Therefore,$a=32$ is the solution of the given equation $\sqrt{a+4}=6$.