2.6 Solving Radical and Rational Exponent Equations

Front

What is a radical expression?

Back

An expression that includes a root, such as a square root or cube root.

Front

What is a rational exponent?

Back

An exponent that can be expressed as a fraction, where the numerator is a power and the denominator is a root.

Front

How do you solve an equation with a square root?

Back

Isolate the square root on one side and then square both sides of the equation.

Front

What is the first step in solving (x + 2)^(1/2) - 5 = -2?

Back

Add 5 to both sides to isolate the square root.

Front

What is the solution to (x + 2)^(1/2) - 5 = -2?

Back

x = 7.

Front

What does it mean to check your solution in radical equations?

Back

Substitute the solution back into the original equation to verify it holds true.

Front

What is the principle of squaring both sides of an equation?

Back

It allows you to eliminate the square root, but you must check for extraneous solutions.

Front

How do you solve m^(1/2) = 2?

Back

Square both sides to get m = 4.

Front

What are extraneous solutions?

Back

Solutions that emerge from the process of solving an equation but do not satisfy the original equation.

Front

What is the solution to m^(1/2) = 2 and m^(1/2) = -2?

Back

m = 4 for the first equation; no solution for the second since square roots cannot be negative.