Certainly! Let's solve the given equation step-by-step:
Given equation:
[tex]\[
\sqrt{x} = 0
\][/tex]
To solve for [tex]\(x\)[/tex], we need to find the value that satisfies this equation.
1. Step 1: Understand the equation
The square root of a number is zero if and only if the number itself is zero. Hence, we must find [tex]\(x\)[/tex] such that:
[tex]\[
\sqrt{x} = 0
\][/tex]
2. Step 2: Square both sides to remove the square root
To isolate [tex]\(x\)[/tex], we square both sides of the equation:
[tex]\[
(\sqrt{x})^2 = 0^2
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the solution to the equation [tex]\(\sqrt{x} = 0\)[/tex] is [tex]\(x = 0\)[/tex].
3. Step 3: Check the given options
We are given several options. Let's verify each one:
- Option A: [tex]\( x = 2 \)[/tex]
[tex]\[
\sqrt{2} \neq 0
\][/tex]
Therefore, [tex]\(2\)[/tex] is not a solution.
- Option B: [tex]\( x = -2 \)[/tex]
[tex]\[
\text{Square roots of negative numbers are not real. So } \sqrt{-2} \text{ is undefined in real numbers.}
\][/tex]
Therefore, [tex]\(-2\)[/tex] is not a solution.
- Option C: [tex]\( x = 0 \)[/tex]
[tex]\[
\sqrt{0} = 0
\][/tex]
Therefore, [tex]\(0\)[/tex] is a solution.
- Option D: [tex]\( x = 15 \)[/tex]
[tex]\[
\sqrt{15} \neq 0
\][/tex]
Therefore, [tex]\(15\)[/tex] is not a solution.
- Option E: [tex]\( x = -16 \)[/tex]
[tex]\[
\text{Square roots of negative numbers are not real. So } \sqrt{-16} \text{ is undefined in real numbers.}
\][/tex]
Therefore, [tex]\(-16\)[/tex] is not a solution.
- Option F: None
Since we have already found that [tex]\( x = 0 \)[/tex] is a valid solution, we do not need to select [tex]\(None\)[/tex].
Based on the above analysis, the correct answer is:
C. 0
