Use the quotient rule to simplify.
$\sqrt{\frac{2}{81}}$

• A. $\frac{\sqrt{2}}{81}$
• B. $\frac{2}{9}$
• C. $\frac{2}{81}$
• D. $\frac{\sqrt{2}}{9}$

Answer: (D)

Verified step by step guidance

1. Recognize that the expression to simplify is \(\sqrt{\frac{2}{81}}\), which means the square root of a fraction.
2. Recall the quotient rule for square roots: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\). Apply this rule to rewrite the expression as \(\frac{\sqrt{2}}{\sqrt{81}}\).
3. Simplify the denominator \(\sqrt{81}\) by finding the square root of 81, which is a perfect square.
4. Rewrite the expression with the simplified denominator, resulting in \(\frac{\sqrt{2}}{9}\).
5. Confirm that the expression cannot be simplified further because \(\sqrt{2}\) is already in simplest radical form.