Solving Radical Equations

Front

What is a radical equation?

Back

An equation that involves a variable within a radical (square root, cube root, etc.).

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, you can move all other terms to the opposite side of the equation.

Front

What is the first step in solving the equation (3x - 5)^(1/4) + 3 = 4?

Back

Subtract 3 from both sides to isolate the radical: (3x - 5)^(1/4) = 1.

Front

What is the next step after isolating the radical (3x - 5)^(1/4) = 1?

Back

Raise both sides to the power of 4 to eliminate the radical: 3x - 5 = 1.

Front

What is the solution to the equation 3x - 5 = 1?

Back

x = 2.

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 the equation (2x - 1)^(3/4) + 9 = 36?

Back

First, subtract 9 from both sides: (2x - 1)^(3/4) = 27.

Front

What is the next step after isolating the radical (2x - 1)^(3/4) = 27?

Back

Raise both sides to the power of 4/3 to eliminate the radical.

Front

What is the solution to the equation (2x - 1) = 27^(4/3)?

Back

x = 41.

Front

What is the importance of checking your solutions in radical equations?

Back

To ensure that the solutions do not produce extraneous results when substituted back into the original equation.