Question

Simplify the radical expression. $$\sqrt{\frac{11}{9}}$$

Short answer

The simplified form of \( \sqrt{\frac{11}{9}} \) is \( \frac{\sqrt{11}}{3} \).

Step-by-step solution

Write the Radicals Separately

We can separate the fraction under the square root into two separate roots. The expression becomes \( \sqrt{11/9} = \sqrt{11} / \sqrt{9} \).

Simplify the Separate Radicals

The square root of 11 remains as it is because 11 is a prime number which doesn't have any perfect square factors. We will denote this as \( \sqrt{11} \). On the other hand, 9 is a perfect square, so its square root is a whole number. Applied square root for 9, which is \( \sqrt{9} = 3 \).

Write Them Together

Combining both results, we can get the final simplified form. So, we can write \( \sqrt{11/9} = \sqrt{11} / \sqrt{9} = \sqrt{11}/3 \).