# Rationalizing the denominatorPage 1

#### WATCH ALL SLIDES

Slide 1 ## Rationalizing

Slide 2 There is an agreement

in mathematics

that we don’t leave a radical

in the denominator

of a fraction.

Slide 3 So how do we change the denominator of a fraction?

(Without changing the value of the fraction, of course.)

Slide 4 The same way we change the denominator of any fraction!

(Without changing the value of the fraction, of course.)

Slide 5 We multiply the denominator

by the same number.

and the numerator

Slide 6 By what number

to a rational number?

to change it

can we multiply

Slide 7 The answer is . . .

. . . by itself!

Slide 8 Remember,

is the number we square

to get n.

we’d better get n.

So when we square it,

Slide 9 Slide 10 Slide 11 Because we are changing the denominator

we call this process rationalizing.

to a rational number,

Slide 12 Rationalize the denominator:

(Don’t forget to simplify)

Slide 13 Rationalize the denominator:

(Don’t forget to simplify)

(Don’t forget to simplify)

Slide 14 When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. This gives a rational denominator.

Slide 15 Multiply by the conjugate.

FOIL numerator and denominator.

Next

Slide 16 Simplify

·

=

Slide 17 Combine like terms