Question

Solve each equation. Check your solution.

$\sqrt{\mathbf{a}\mathbf{+}\mathbf{4}}\mathbf{=}\mathbf{6}$

Short answer

The solution of the given equation is$\mathit{a}\mathbf{=}\mathbf{32}$.

Check:

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

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

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

Step-by-step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

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

Step 2. Solve the given equation.

The solution of the given equation is:

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

Therefore, the value$a$ is 32.

Step 3. Check the solution.

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

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

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