Solving Radical Equations

Front

What is a radical equation?

Back

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

Tags

CCSS.HSA.REI.A.2

Front

How do you solve a radical equation?

Back

Isolate the radical on one side, then square both sides to eliminate the radical, and solve for the variable.

Tags

CCSS.HSA.REI.A.2

Front

Why is it important to check your answers when solving radical equations?

Back

To ensure that the solutions are valid, as squaring both sides can introduce extraneous solutions.

Tags

CCSS.HSA.REI.A.2

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving the equation but does not satisfy the original equation.

Tags

CCSS.HSA.REI.A.2

Front

What is the first step in solving the equation √(x + 3) = 5?

Back

Square both sides to eliminate the radical: x + 3 = 25.

Tags

CCSS.HSA.REI.A.2

Front

Solve the radical equation: √(x - 1) = 4.

Back

x = 17.

Tags

CCSS.HSA.REI.A.2

Front

Solve the radical equation: √(2x + 4) = 6.

Back

x = 14.

Tags

CCSS.HSA.REI.A.2

Front

What does it mean to isolate the radical in an equation?

Back

To rearrange the equation so that the radical expression is alone on one side.

Tags

CCSS.HSA.REI.A.2

Front

Solve the radical equation: √(x + 2) = x - 2.

Back

x = 4.

Tags

CCSS.HSA.REI.A.2

Front

What is the solution to the equation √(x) = -3?

Back

No solution, as the square root cannot be negative.

Tags

CCSS.HSA.REI.A.2