Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Aim: How do we rationalize a denominator? Do Now: Factor completely: 2x 2 – 50.

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Presentation transcript:

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Aim: How do we rationalize a denominator? Do Now: Factor completely: 2x 2 – 50

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. General Terms Conjugates conjugates of each other (a – b)(a + b) a 2 – b 2 = (x + 6) What is the conjugate of (x – 6) When conjugates are multiplied, the result is the difference between perfect squares. 2x = 2(x – 5)(x + 5) = x 2 – 36 = x 2 – 5 = 9 – 7 = 2

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Rational & Irrational Numbers Rational Numbers - Any number, integer, fraction, decimal;positive or negative, mixed or improper, that can be expressed as a fraction. Every rational number can be expressed as either a repeating or terminating decimal. Ex. 2, 1.765, 1/2, 0.33 Irrational Numbers - Any and all numbers that can not be expressed as a fraction. Ex  = =

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Rational Numbers Rational Numbers a/b Integers Integers... -3, -2, -1, 0, 1, 2, 3,.. Whole Numbers Whole Numbers 0, 1, 2, 3, 4, 5,.. Irrational Numbers Irrational Numbers a/b Counting Numbers Counting Numbers 1, 2, 3, 4, 5,... Real Number Family

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Rationalizing a Monomial Denominator Multiply fraction by a form of the identity element 1. Simplify the radical, if possible means to remove the irrational number from the denominator rational number irrational number

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Rationalizing a Denominator (of a fraction where the denominator is not a rational number) means to find a denominator in which the denominator is a rational number. How can we use the conjugate to rationalize (a – b)(a + b) a 2 – b 2 =   Multiply fraction by a form of the identity element 1. binomial denominator

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Model Problems Rationalize the denominator: Express as an equivalent fraction with a rational denominator. Write an equivalent expression for 3

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Model Problems Simplify/Rationalize:

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Model Problems Simplify/Rationalize:

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Model Problems Simplify/Rationalize:

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Model Problems Simplify/Rationalize:

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Model Problems Simplify/Rationalize:

Aim: Rationalize Denominator Course: Adv. Alg. & Trig. Model Problems Simplify/Rationalize: