Solving Radical Equations by factoring

Front

What is a radical equation?

Back

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

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, move all other terms to the opposite side of the equation.

Front

What is the first step in solving the equation x = √2x?

Back

Square both sides to eliminate the square root.

Front

What are extraneous solutions in radical equations?

Back

Solutions that emerge from the process of solving the equation but do not satisfy the original equation.

Front

What is the solution to the equation x - 7 = √5x - 41?

Back

x = 10, 9.

Front

What does it mean if a radical equation has no solution?

Back

It means that there are no values for the variable that satisfy the equation.

Front

How do you check if a solution is valid in a radical equation?

Back

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

Front

What is the solution to the equation √-10x-25 = x?

Back

no solution.

Front

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

Back

It helps to eliminate the radical, making the equation easier to solve.

Front

What is the solution to the equation k = √-11k -24?

Back

no solution.