Answer :
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.
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.
