Simplify. $$ \sqrt{\frac{9}{81}} $$ Be sure to write your answer in simplest form.

Question

UpStudy AI · Accepted Answer

To simplify the expression $$\sqrt{\frac{9}{81}}$$, follow these steps:

1. **Simplify the Fraction Inside the Square Root:**

$$
   \frac{9}{81} = \frac{1}{9}
   $$
   
   (Since both the numerator and the denominator can be divided by 9.)

2. **Take the Square Root:**

$$
   \sqrt{\frac{1}{9}} = \frac{\sqrt{1}}{\sqrt{9}} = \frac{1}{3}
   $$
   
   (Because $$\sqrt{1} = 1$$ and $$\sqrt{9} = 3$$.)

So, the expression $$\sqrt{\frac{9}{81}}$$ simplifies to:

$$
\frac{1}{3}
$$
$$\frac{1}{3}$$

Simplify. \[ \sqrt{\frac{9}{81}} \] Be sure to write your answer in simplest form.