The Principle of Powers
A radical equation is an equation in which a variable appears in a
For example, the variable x is in the radicand of the following radical
To solve a radical equation, we will use the Principle of Powers.
Principle â€” Principle of Powers
If a = b, then an = bn
Here, a, b, and n are real numbers.
While the Principle of Powers is true for all real numbers, the reverse is
not always true. That is, if an = bn then a = b may or may not be true.
For example, consider the following equations.
|Square both sides.
is the principle or positive
square root of x. This is a positive number
The solution of Equation A, x = 25, checks since
However, the solution of Equation B, x = 25, does NOT check
Squaring both sides of Equation B introduced an extraneous solution or
false solution. Thus, when solving a radical equation we must check the
answer to verify that it satisfies the original equation.
The negative square root of x is written as
-. This is a negative number.