Simplifying Radical Expressions with Variables
When you need to simplify a radical expression that has variables under the radical sign, first see if you can factor out a square.
Since a negative number times a negative number is always a positive number, you need to remember when taking a square root that the answer will be both a positive and a negative number or expression. For example , and also . We usually will denote such dual answers as .
Factor the radicand as the product of and a squared expression.
Use the product property of square roots :
Rewrite the radicand using squared expressions where possible.
Simplify. The square roots of and can be negative or positive, so use the sign .