Simplifying Radical Expressions Containing One Term

Example

Simplify:

Solution

This radical expression is not in simplified form because it has a radical in its denominator.

To begin, we will write the expression as a quotient under a single radical symbol.

Then we will try to simplify that quotient so that it can be written without a denominator.

Use the Division Property of Radicals to write the quotient under one radical symbol.
Simplify the radicand.
We have rewritten the radicand without a denominator. However, the radicand has some factors that are perfect squares.
Factor the radicand. Use perfect square factors when possible.
Write as a product of radicals. Place each perfect square under its own radical symbol.
Simplify the square root of each perfect square.
Multiply the factors outside the radical symbol.
So,