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 isolate a variable in a radical equation?

Back

Square both sides of the equation to eliminate the radical, then solve for the variable.

Tags

CCSS.HSA.REI.A.2

Front

What is the first step in solving the equation √(x + 5) = 7?

Back

Square both sides to get x + 5 = 49.

Tags

CCSS.HSA.REI.A.2

Front

What is the solution to the equation √(x + 5) = 7?

Back

x = 44.

Tags

CCSS.HSA.REI.A.2

Front

What should you do after solving a radical equation?

Back

Check your solution by substituting it back into the original equation.

Tags

CCSS.HSA.REI.A.2

Front

What is the extraneous solution in radical equations?

Back

A solution that does not satisfy the original equation after substitution.

Tags

CCSS.HSA.REI.A.2

Front

Solve the equation √(2x - 3) = 5.

Back

x = 14.

Tags

CCSS.HSA.REI.A.2

Front

What is the domain of the function f(x) = √(x - 2)?

Back

x must be greater than or equal to 2.

Front

How do you solve the equation √(x + 1) + 3 = 6?

Back

Isolate the radical: √(x + 1) = 3, then square both sides to find x = 8.

Tags

CCSS.HSA.REI.A.2

Front

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

Back

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

Tags

CCSS.HSA.REI.A.2