Do Now You have 5 minutes a b

Do Now: You have 5 minutes. a. b. c. d.

Focus Question: How can we rationalize the denominator containing a radical expression? October 10, 2013

There is an agreement in mathematics that we don’t leave a radical in the denominator of a fraction.

If we tried to write as a decimal, we would not be able to. • We cannot divide by a non-terminating decimal number. We must rationalize the denominator.

We must RATIONALIZE THE DENOMINATOR!!! • Definition: To rationalize the denominator means to rewrite the fraction so the denominator is a rational number. We must use a number’s conjugate for this.

Conjugate: • Definition: Numbers are conjugates of one another if they solve the same irreducible polynomial equation. Examples of conjugate pairs:

Find the conjugates of the following irrational numbers:

Rationalize the Denominator: Tip: If the denominator is a simple radical (like it is here), you can just multiply by itself to avoid dealing with the negative sign.

Rationalize the denominator: (D f t ’ n o t e g r o m i s to ) y f i l p

Rationalize the denominator: t e g r o f t ’ n o (D (D f t ’ n o t e g r o m i s to ) y f i l p

Simplify: Multiply by the conjugate. FOIL numerator and denominator. Next

Combine like terms Try this on your own:

Simplify · =