To solve the equation [tex]\(\sqrt{x} + \sqrt{9} = \sqrt{121}\)[/tex], follow these steps:
1. Simplify the known square roots:
[tex]\[
\sqrt{9} = 3 \quad \text{and} \quad \sqrt{121} = 11
\][/tex]
2. Substitute these values into the equation:
[tex]\[
\sqrt{x} + 3 = 11
\][/tex]
3. Isolate [tex]\(\sqrt{x}\)[/tex] by subtracting 3 from both sides:
[tex]\[
\sqrt{x} = 11 - 3
\][/tex]
[tex]\[
\sqrt{x} = 8
\][/tex]
4. Square both sides of the equation to solve for [tex]\(x\)[/tex]:
[tex]\[
(\sqrt{x})^2 = 8^2
\][/tex]
[tex]\[
x = 64
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{64}\)[/tex].
