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Solve the equation. Check your solution.

[tex]\[
\sqrt{z+7} = 6
\][/tex]

[tex]\[ z = [?] \][/tex]

Sagot :

GinnyAnswer
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.
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