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; 𝑎𝑏 =
• Quotient Property;
𝑎
𝑏
=
𝑎 𝑏
𝑎
𝑏
• 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 18
• Perfect root that is a factor of 18?
• Example. Simplify 45
• Example. Simplify 20
• Example. Simplify 2 12
Rationalizing
• If a fraction has a square root in the denominator, we will eliminate
the radical by rationalizing
• For a number a, 𝑎 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
1
9
• Example. Simplify the expression
36
49
• Example. Simplify the expression
7
11
• Example. Simplify the expression
18
5
• Simplify the following expressions together.
• 1) 5 20
• 2) 12 3
• 3)
• 4)
9
64
2
5
• Assignment
• Pg. 258
• 18 – 44 even