Rationalizing the denominator

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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

Try this on your own: