To solve the equation \(\sqrt{z + 7} = 6\), follow these steps:
1. Square both sides of the equation to eliminate the square root:
[tex]\[
(\sqrt{z + 7})^2 = 6^2
\][/tex]
This simplifies to:
[tex]\[
z + 7 = 36
\][/tex]
2. Isolate \(z\) by subtracting 7 from both sides of the equation:
[tex]\[
z = 36 - 7
\][/tex]
Thus, we find:
[tex]\[
z = 29
\][/tex]
To verify our solution, we will check if \(z = 29\) satisfies the original equation \(\sqrt{z + 7} = 6\):
1. Substitute \(z = 29\) back into the original equation:
[tex]\[
\sqrt{29 + 7} = 6
\][/tex]
Simplify inside the square root:
[tex]\[
\sqrt{36} = 6
\][/tex]
2. Then, calculate \(\sqrt{36}\):
[tex]\[
6 = 6
\][/tex]
Since both sides of the equation are equal, our solution [tex]\(z = 29\)[/tex] is correct.
