5.6.1 – Square Root Method

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