Solving Radical Equations

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What is a radical equation?

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

Tags

CCSS.HSA.REI.A.2

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How do you isolate a radical in an equation?

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To isolate a radical, you can move all other terms to the opposite side of the equation and simplify.

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CCSS.HSA.REI.A.2

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Multiply both sides by 2 to eliminate the fraction.

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CCSS.7.EE.B.4A

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What does it mean to check for extraneous solutions?

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

Tags

CCSS.HSA.REI.A.2

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x = 7.

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CCSS.7.EE.B.4A

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What is the square root property?

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CCSS.HSA-REI.B.4B

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x = 4 or x = -4.

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CCSS.8.EE.A.2

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

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

Tags

CCSS.HSA.REI.A.2

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x = 4.

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What is an extraneous solution?

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An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Tags

CCSS.HSA.REI.A.2