Answer :
To solve the equation [tex]\(\sqrt{x} = 9\)[/tex], we'll start by finding the value of [tex]\(x\)[/tex].
Step 1: Eliminate the square root by squaring both sides of the equation:
[tex]\[
(\sqrt{x})^2 = 9^2
\][/tex]
Step 2: Since squaring a square root cancels it out, you're left with:
[tex]\[
x = 9^2
\][/tex]
Step 3: Calculate [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 81
\][/tex]
Thus, [tex]\(x = 81\)[/tex].
Now, let's check each option to see which one matches our solution:
- Option A: 0
0 is not equal to 81
- Option B: -3
-3 is not equal to 81
- Option C: 81
81 matches our solution
- Option D: 3
3 is not equal to 81
- Option E: -81
-81 is not equal to 81
- Option F: None
Since we found a solution (81), this option is not correct.
Therefore, the correct solution is option C: 81.
Step 1: Eliminate the square root by squaring both sides of the equation:
[tex]\[
(\sqrt{x})^2 = 9^2
\][/tex]
Step 2: Since squaring a square root cancels it out, you're left with:
[tex]\[
x = 9^2
\][/tex]
Step 3: Calculate [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 81
\][/tex]
Thus, [tex]\(x = 81\)[/tex].
Now, let's check each option to see which one matches our solution:
- Option A: 0
0 is not equal to 81
- Option B: -3
-3 is not equal to 81
- Option C: 81
81 matches our solution
- Option D: 3
3 is not equal to 81
- Option E: -81
-81 is not equal to 81
- Option F: None
Since we found a solution (81), this option is not correct.
Therefore, the correct solution is option C: 81.
