Radical Equations

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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.).

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Square both sides to eliminate the radicals: \(3x + 12 = x + 8\). Then, solve for x to find \(x = -2\).

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The domain is \([1, \infty)\) because the expression under the square root must be non-negative.

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The range is \([0, \infty)\) because the output of a square root function is always non-negative.

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How do you find the domain of a radical function?

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Set the expression inside the radical greater than or equal to zero and solve for x.

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What does the symbol ( ) indicate in interval notation?

Back

It indicates that the endpoint is not included in the interval.

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What does the symbol [ ] indicate in interval notation?

Back

It indicates that the endpoint is included in the interval.

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Add 8 to both sides: \(\sqrt{5x - 5} = 5\). Square both sides: \(5x - 5 = 25\). Solve for x: \(x = 6\).

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The simplified form is \(2\sqrt{30}\).

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What is the first step in solving a radical equation?

Back

Isolate the radical on one side of the equation.