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.).

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.

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Back

Multiply both sides by 2 to eliminate the fraction.

Front

What does it mean to check for extraneous solutions?

Back

Checking for extraneous solutions means verifying that the solutions found satisfy the original equation, as some operations may introduce false solutions.

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Back

x = 7.

Front

What is the square root property?

Back

Front

Back

x = 4 or x = -4.

Front

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

Back

Squaring both sides can help eliminate radicals, but it may also introduce extraneous solutions.

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Back

x = 4.

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.