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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q39. (page 729)

Solve each equation. Check your solution.
$\sqrt{a + 4} = 6$

Short Answer

Expert verified

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

Check:

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

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

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

Step by step solution

01

Step 1. Rewrite the given equation.

The given equation can be written as:

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

02

Step 2. Solve the given equation.

The solution of the given equation is:

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

Therefore, the value $a$ is 32.

03

Step 3. Check the solution.

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

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

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

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