5.6.1 – Square Root Method. Recall, we solved “quadratic equations” when we set a polynomial...
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Transcript of 5.6.1 – Square Root Method. Recall, we solved “quadratic equations” when we set a polynomial...
5.6.1 – Square Root Method
• Recall, we solved “quadratic equations” when we set a polynomial equation equal to 0
• Example. x2 + 5x + 6 = 0
• In some cases, we can use a special method to solve the equations• So far we have used factoring, calculators, quadratic equation
Properties of Square Roots
• Before we start to solve them using the new method, there are some basic properties of square roots we should know
• Product Property; • Quotient Property; • In a fraction, you may not have a radical in the denominator (bottom)
Simplifying/Rationalizing
• To simplify a radical expression, we will look for any perfect square roots we could pull out• Perfect Roots = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,…• If there are no perfect roots to pull out, then the expression is
considered simplified
• Example. Simplify • Perfect root that is a factor of 18?
• Example. Simplify
• Example. Simplify
• Example. Simplify
Rationalizing
• If a fraction has a square root in the denominator, we will eliminate the radical by rationalizing • For a number a, = a• To eliminate the radical, multiply top and bottom by the radical itself• Be sure to simplify the top as necessary
• Example. Simplify the expression
• Example. Simplify the expression
• Example. Simplify the expression
• Example. Simplify the expression
• Simplify the following expressions together.
• 1)
• 2)
• 3)
• 4)
• Assignment• Pg. 258• 18 – 44 even