To simplfy, we must first distribute the square root.

Next, we can simplify each of the square roots.

Simplify each radical:

Rationalize the denominator:

√27 is the same as 3√3, while √12 is the same as 2√3.

3√3 + 2√3 = 5√3

(5√3)/(√3) = 5

Find the quotient:

There are two ways to approach this problem.

Option 1: Combine the radicals first, the reduce

Option 2: Simplify the radicals first, then reduce

There are two ways to solve this problem. First you can divide the numbers under the radical. Then simplify.

Example 1

Example 2

Find the square root of both numerator and denominator, simplifying as much as possible then dividing out like terms.

Both methods will give you the correct answer of .