**SOLVING RADICAL EQUATIONS**

**The Principle of Powers**

A **radical equation **has variables in one or more radicands—for example,

+ 1 = 5, + = 7.

To solve such an equation, we need a new equation-solving principle. Suppose

that an equation a = b is true. If we square both sides, we get another

true equation: a^{2} = b^{2}. This can be generalized.

**THE PRINCIPLE OF POWERS**

For any natural number n, if an equation a = b is true, then a^{n} = b^{n} is true.

However, if an equation a^{n} = b^{n } is true, it *may not *be true that a = b, if *n*

is even. For example, 3^{2} = (-3)^{2} is true, but 3 = -3 is not true. Thus we *must*

make a check when we solve an equation using the principle of powers.