Conjugate: Value or that is multiplied to a radical expressionThat clears the radical.

Rationalizing: Removing a radical expression from the denominator of a fraction.Process: Multiply the fraction by a factor of one its conjugate of denominator.

Example 1 Rationalizing Square Roots[A]

35 [B]

57

SIMPLIFYING QUOTIENTS OF RADICALS

_NUMERATOR_DENOMINATOR

Conjugate of DenominatorConjugate of Denominator _NUMERATOR_

DENOMINATOR

Example 2 Rationalizing Square Roots Continued

[A]3

5x

[B]52

7x

Example 3 Rationalizing Cube Roots

[A]3

2

27x

[B]3

7

3x

[C]3

4

125x

[D]3

10

5x

Example 4 Tougher Rationalizing

[A]

yx 3

5 [B]3

108

5yx

[1] [2] [3] [4]

[5] [6] [7] [8]

[9] [10] [11] [12]

PRACTICE - Simplifying Radicals: Use as separate paper. 237

51

453 3213 1515

73

3yx

5

3x

37

5x

314

10y

3114

2yx5

15xy

Binomial Conjugate:

Binomial that differ only by an addition or subtraction of terms.

y2 x5

The product of binomial conjugates is a difference of squares (FOIL) .

2222 babababababa

[1] [2]

Example 1: Use Binomials Conjugates to Rationalize

[A]35

2

[B]51

7

Example 2: Use Binomials Conjugates to Rationalize

[A]52

1 726

25[B]