Let's solve the equation
[tex]\[
\sqrt{x} + 3 = 12
\][/tex]
step by step.
1. Isolate the square root term:
Subtract 3 from both sides of the equation to isolate the square root term:
[tex]\[
\sqrt{x} = 12 - 3
\][/tex]
Simplifying the right-hand side gives us:
[tex]\[
\sqrt{x} = 9
\][/tex]
2. Eliminate the square root:
To eliminate the square root, square both sides of the equation:
[tex]\[
(\sqrt{x})^2 = 9^2
\][/tex]
This simplifies to:
[tex]\[
x = 81
\][/tex]
3. Verify the solution:
Substitute [tex]\( x = 81 \)[/tex] back into the original equation to ensure it satisfies the equation:
[tex]\[
\sqrt{81} + 3 = 12
\][/tex]
Since [tex]\(\sqrt{81} = 9\)[/tex], the left-hand side becomes:
[tex]\[
9 + 3 = 12
\][/tex]
Since [tex]\(12 = 12\)[/tex], our solution is verified.
Thus, the solution to the equation [tex]\(\sqrt{x} + 3 = 12\)[/tex] is [tex]\(x = 81\)[/tex], making the correct answer:
[tex]\[
\boxed{81}
\][/tex]
