To find which expression is equivalent to the given radical expression [tex]\(\sqrt{\frac{3}{64}}\)[/tex] when it is simplified, let's go through the steps of simplification.
1. Rewrite the Radical Expression:
The given expression is [tex]\(\sqrt{\frac{3}{64}}\)[/tex].
2. Apply the Property of Square Roots:
We can use the property of square roots that states:
[tex]\[
\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}
\][/tex]
Applying this to our expression:
[tex]\[
\sqrt{\frac{3}{64}} = \frac{\sqrt{3}}{\sqrt{64}}
\][/tex]
3. Simplify the Denominator:
Next, we simplify [tex]\(\sqrt{64}\)[/tex]. Since [tex]\(64\)[/tex] is a perfect square:
[tex]\[
\sqrt{64} = 8
\][/tex]
So, the expression now becomes:
[tex]\[
\frac{\sqrt{3}}{8}
\][/tex]
4. Comparison to Options:
Having simplified the original expression to [tex]\(\frac{\sqrt{3}}{8}\)[/tex], we compare this to the given options:
- A. [tex]\(\frac{3}{64}\)[/tex]: This does not match [tex]\(\frac{\sqrt{3}}{8}\)[/tex].
- B. [tex]\(\frac{\sqrt{3}}{8}\)[/tex]: This matches our simplified expression.
- C. [tex]\(\frac{3}{8}\)[/tex]: This does not match [tex]\(\frac{\sqrt{3}}{8}\)[/tex].
- D. [tex]\(\frac{\sqrt{3}}{64}\)[/tex]: This does not match [tex]\(\frac{\sqrt{3}}{8}\)[/tex].
Therefore, the correct equivalent expression is:
[tex]\[
\boxed{\frac{\sqrt{3}}{8}}
\][/tex]
So the correct answer is B. [tex]\(\frac{\sqrt{3}}{8}\)[/tex].
