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 square root in an equation?

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To isolate a square root, you can move all other terms to the opposite side of the equation and then square both sides to eliminate the radical.

Tags

CCSS.HSA.REI.A.2

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x = 10

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CCSS.6.EE.B.7

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CCSS.HSA.REI.A.2

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x = 16.

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What does it mean if a radical equation has no solution?

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It means that there are no values for the variable that satisfy the equation, often due to taking the square root of a negative number.

Tags

CCSS.HSA.REI.A.2

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x = 25.

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No solution, because the square root of a number cannot be negative.

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x = 13.

Tags

CCSS.HSA.REI.A.2

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

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Squaring both sides can eliminate a square root, but it may introduce extraneous solutions that need to be checked.

Tags

CCSS.HSA.REI.A.2