Solving Radicals

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

Front

What is the principal square root?

Back

The principal square root of a number is the non-negative root. For example, the principal square root of 9 is 3, denoted as @@ ext{ } oot{2}{9} = 3@@.

Front

How do you solve a radical equation?

Back

To solve a radical equation, isolate the radical on one side and then square both sides to eliminate the radical. Check for extraneous solutions afterward.

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

Solve the radical equation: @@ ext{ } oot{2}{x} = 4@@.

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Front

Solve the radical equation: @@ ext{ } oot{3}{x} = 3@@.

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Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all input values (x) for which the expression under the radical is non-negative.

Front

Solve the radical equation: @@ ext{ } oot{2}{x + 3} = 5@@.

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Front

What is the first step in solving @@ ext{ } oot{2}{x + 12} - 9 = -6@@?

Back

Isolate the radical: @@ ext{ } oot{2}{x + 12} = 3@@.

Front

Solve the radical equation: @@ ext{ } oot{2}{2x + 5} + 4 = 7@@.

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