To simplify the given radical expression \( \sqrt{\frac{3}{64}} \), we need to follow these steps:
1. Separate the Square Root:
The square root of a fraction can be written as the square root of the numerator over the square root of the denominator. Therefore,
[tex]\[
\sqrt{\frac{3}{64}} = \frac{\sqrt{3}}{\sqrt{64}}
\][/tex]
2. Simplify the Denominator:
Find the square root of the denominator:
[tex]\[
\sqrt{64} = 8
\][/tex]
3. Write the Simplified Expression:
Now, substitute back the simplified square root of the denominator into the fraction:
[tex]\[
\frac{\sqrt{3}}{8}
\][/tex]
Therefore, the simplified form of the given radical expression \( \sqrt{\frac{3}{64}} \) is \(\frac{\sqrt{3}}{8}\).
Thus, the correct answer is:
D. [tex]\(\frac{\sqrt{3}}{8}\)[/tex].
