Solving Radicals Equations

Front

Define a radical equation.

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

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Back

Front

How do you eliminate a square root in an equation?

Back

Square both sides of the equation to eliminate the square root.

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Back

x = 1.

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Back

x = 25.

Front

Explain the importance of checking your solutions in radical equations.

Back

Checking solutions is crucial because squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

Front

Back

x = 18.

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 on one side of an equation?

Back

Use algebraic operations (addition, subtraction, multiplication, division) to move other terms to the opposite side.

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Back

x = 16.