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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
We need to find the two square roots of $$\frac{1}{16}$$.
This means finding two numbers that, when multiplied by themselves, equal \frac{1}{16}.
Step 3:: Set Up the Square Root Equation
x^{2} = \frac{1}{16}
We want to solve the equation:
Step 4:: Solve for x
x = \pm\sqrt{\frac{1}{16}}
To solve this, we'll take the square root of both sides:
Step 5:: Simplify the Square Root
x = \pm\frac{1}{4}
Step 6:: Verify the Solutions
- Negative root: $$(-\frac{1}{4})^{2} = \frac{1}{16}$$ ✓
Let's check both values:
Final Answer
The two square roots of \frac{1}{16} are \frac{1}{4} and -\frac{1}{4}.
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