Solving Radical Equations

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained 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 and simplify if necessary.

Tags

CCSS.HSA.REI.A.2

Front

What is the first step in solving a radical equation?

Back

The first step is to isolate the radical on one side of the equation.

Tags

CCSS.HSA.REI.A.2

Front

What does it mean to check for extraneous solutions?

Back

Checking for extraneous solutions means substituting the found solutions back into the original equation to verify if they satisfy it.

Tags

CCSS.HSA.REI.A.2

Front

What is an extraneous solution?

Back

An extraneous solution is 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

How do you solve the equation \(\sqrt{4x - 4} = x - 1\)?

Back

Square both sides to eliminate the radical, leading to \(4x - 4 = (x - 1)^2\), then solve for x.

Tags

CCSS.HSA.REI.A.2

Front

What are the possible solutions for the equation \(\sqrt{4x - 4} = x - 1\)?

Back

The possible solutions are x = 1 and x = 5.

Tags

CCSS.HSA.REI.A.2

Front

What is the solution to the equation \(\sqrt{x + 4} = x - 2\)?

Back

The solution is x = 5, but x = 0 is an extraneous solution.

Tags

CCSS.HSA.REI.A.2

Front

What is the importance of squaring both sides of a radical equation?

Back

Squaring both sides helps eliminate the radical, allowing for easier manipulation and solving of the equation.

Tags

CCSS.HSA.REI.A.2

Front

What should you do if you encounter a radical equation with no solution?

Back

If there is no solution, it means that the equation does not hold true for any value of the variable.

Tags

CCSS.HSA.REI.A.2