Solving Radical Equations

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What is a radical equation?

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

Tags

CCSS.HSA.REI.A.2

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What is the first step in solving the equation @@ \sqrt{3y + 4} = 5@@?

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Square both sides.

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CCSS.HSA.REI.A.2

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Back

x = 36.

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CCSS.HSA.REI.A.2

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Back

z = 25.

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What does it mean to isolate the variable in an equation?

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To manipulate the equation so that the variable is on one side and all other terms are on the other side.

Tags

CCSS.7.EE.B.4A

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

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It allows you to eliminate the square root, but you must check for extraneous solutions.

Tags

CCSS.HSA.REI.A.2

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n = 0.

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CCSS.HSA.REI.A.2

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What is an extraneous solution?

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A solution that emerges from the process of solving the equation but does not satisfy the original equation.

Tags

CCSS.HSA.REI.A.2

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n = 4.

Tags

CCSS.HSA.REI.A.2

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What is the domain of a radical function?

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The set of all possible input values (x) for which the function is defined, typically requiring the expression under the radical to be non-negative.