Pre-Calculus 11 Multiplying & Dividing Radical Expressions

Lesson Focus: To perform multiple operations on radical expressions; to rationalize the denominator; to solve

problems that involve radical expressions.

when multiplying radicals with the same indices, multiply the coefficients and multiply the radicands

i.e. kkk banmbnam where k is a natural number and m, n, a and b are real numbers

if the index, k, is even, then 0 and 0 ba

when multiplying radicals with more than one term, use the distributive property and simplify

e.g. Simplify.

1. 10653 2. 0,72144 3 xxx

3. 61053 4. 0,524525 xxxx

when dividing two radicals with the same indices, divide the coefficients and divide the radicands

i.e. kk

k

b

a

n

m

bn

am

where k is a natural number, m, n, a and b are real numbers and 0 and 0 bn

if k is even, then 0 and 0 ba

e.g. Simplify.

1. 22

614 2. 0,0,

53

1562

2

yxxyx

xyxy

to rationalize the denominator, write an equivalent in which the denominator is a rational number

multiply the top and the bottom of the fraction by the radical in the denominator

i.e

2

23

2

2

2

3

2

3

e.g. Simplify.

1. 32

58 2.

x24

76

conjugates are two binomial factors whose product is the difference of two squares

to find the conjugate of a binomial, reverse the sign of the second term in the binomial

multiplying the binomials together will create a difference of squares, which will result in a rational number

i.e. binomial: 64 conjugate: 64

10

616

366464166464

in order to rationalize the denominator when it contains a square root binomial:

1. find the conjugate of the denominator

2. multiply the numerator and denominator by the conjugate

3. simplify

i.e.

10

6312

64

64

64

3

64

3

e.g. Simplify. Rationalize the denominator.

1. 72

4

2.

235

7