CLO and Warm Up

I will be able to rationalize the denominators and numerators of radical expressions.

Warm UP:Simplify:

7.5

Rationalizing Denominators and

Numerators of Radical

Expressions

Many times it is helpful to rewrite a radical quotient with the radical confined to ONLY the numerator.

If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator.

This process involves multiplying the quotient by a form of 1 that will eliminate the radical in the denominator.

Rationalizing Denominators

Rationalize the denominator.

a.

b.

23

22

3 96

3

3

33

2223

26

33

3

393 6

3

3

273 6

3

3 6 33 3 2

Example

Rationalize the denominator.

73xy

Example

73

xy

7

3

3

3

yx

y y

213

xyy

Rationalize the denominator.4

54 81

xy

Example

4

44 481

x

y y

4

43

xy y

4

4

4

34

3

3

y y

y

y

x

34

443

xy

y y

34

23

xyy

Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical.

In that case, we need to multiply by the conjugate of the numerator or denominator (which ever one we are rationalizing).

The conjugate uses the same terms, but the opposite operation (+ or –).

Conjugates

Rationalize the denominator.

3 22 3

2 32 3

6 3 2 2 2 32 3

6 3 2 2 2 31

6 3 2 2 2 3

Example

3 2 3 2 2 2 32 2 3 2 3 3

Homework

Pg. 445 #1 - 10 all and #41 – 45 all