Simplify. $$ \sqrt{\frac{36}{81}} $$ Be sure to write your answer in simplest form.

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UpStudy AI · Accepted Answer

1. Write the square root of a fraction as the fraction of square roots:
   $$
   \sqrt{\frac{36}{81}} = \frac{\sqrt{36}}{\sqrt{81}}
   $$

2. Evaluate the square roots:
   $$
   \sqrt{36} = 6 \quad \text{and} \quad \sqrt{81} = 9
   $$
   So,
   $$
   \frac{\sqrt{36}}{\sqrt{81}} = \frac{6}{9}
   $$

3. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:
   $$
   \frac{6 \div 3}{9 \div 3} = \frac{2}{3}
   $$

Thus, the simplified form is:
$$
\boxed{\frac{2}{3}}
$$
$$ \frac{2}{3} $$

Simplify.

Be sure to write your answer in simplest form.

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Simplify. Be sure to write your answer in simplest form.