Solving Radical Equations Extraneous Solutions

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (root) symbol.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

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 (∛4n - 8) - 4 = 0?

Back

Add 4 to both sides to isolate the cube root: ∛4n - 8 = 4.

Front

What is the next step after isolating the radical in (∛4n - 8) = 4?

Back

Cube both sides to eliminate the cube root: 4n - 8 = 64.

Front

What is the solution to the equation 4n - 8 = 64?

Back

n = 18.

Front

How do you check for extraneous solutions?

Back

Substitute the solution back into the original equation to see if it holds true.

Front

What is the first step in solving the equation 2 + (√3y - 5) = 10?

Back

Subtract 2 from both sides to isolate the square root: √3y - 5 = 8.

Front

What do you do after isolating the square root in √3y - 5 = 8?

Back

Add 5 to both sides: √3y = 13.

Front

What is the next step after isolating the square root in √3y = 13?

Back

Square both sides to eliminate the square root: 3y = 169.