Rationalizing the Denominator When Solving Quadratic Equations Using the Square Root Property
When applying the Square Root Property to solve a quadratic equation, the resulting solutions may contain fractions inside the radicals. If taking the square root produces an irrational number in the denominator, the denominator must be rationalized to write the final solutions in standard simplified form. First, use the Quotient Property of Square Roots to rewrite the square root of the fraction as the quotient of two separate square roots. Then, multiply both the numerator and the denominator by the appropriate radical to eliminate the square root from the denominator. For example, when solving , dividing by 2 gives . Applying the Square Root Property yields . Rewriting this as gives . To rationalize the denominator, multiply the numerator and denominator by to obtain the final simplified solutions .
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Ch.9 Quadratic Equations and Functions - Intermediate Algebra @ OpenStax
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Rationalizing the Denominator When Solving Quadratic Equations Using the Square Root Property
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