Solving Radical Equations

Front

What is a radical equation?

Back

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

Tags

CCSS.HSA.REI.A.2

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.

Tags

CCSS.HSA.REI.A.2

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.

Tags

CCSS.HSA.REI.A.2

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.

Tags

CCSS.HSA.REI.A.2

Front

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

Back

x = 2.

Tags

CCSS.7.EE.B.4A

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.

Tags

CCSS.HSN.RN.A.2

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.

Tags

CCSS.HSA.REI.A.2

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.

Tags

CCSS.HSA.REI.A.2