Certainly! To find the value of [tex]\(\sqrt{\frac{1}{64}}\)[/tex], let's break it down step by step.
1. Start with the fraction inside the square root: [tex]\(\frac{1}{64}\)[/tex].
2. Understand that taking the square root of a fraction is the same as taking the square root of the numerator and the denominator separately:
[tex]\[
\sqrt{\frac{1}{64}} = \frac{\sqrt{1}}{\sqrt{64}}
\][/tex]
3. Calculate the square root of the numerator, which is 1:
[tex]\[
\sqrt{1} = 1
\][/tex]
4. Next, calculate the square root of the denominator, which is 64:
[tex]\[
\sqrt{64} = 8
\][/tex]
5. Now, place the square roots back into the fraction:
[tex]\[
\frac{\sqrt{1}}{\sqrt{64}} = \frac{1}{8}
\][/tex]
So, the value of [tex]\(\sqrt{\frac{1}{64}}\)[/tex] is:
[tex]\[
\sqrt{\frac{1}{64}} = \frac{1}{8}
\][/tex]
Given in decimal form:
[tex]\[
\sqrt{\frac{1}{64}} = 0.125
\][/tex]
Therefore, the correct choice is:
[tex]\(\sqrt{\frac{1}{64}} = 0.125\)[/tex]
