Multiplying and Dividing Radicals'

5.2 ? Mulitplying and Dividing Radicals(Solutions).notebook

October 19, 2015

5.2 ?

MULTIPLYING

AND DIVIDING

RADICAL

EXPRESSIONS

Multiplying and Dividing Radicals'

Rules

1.

Simplify the radical before multiplication.

2.

The radicals must have the same index.

3.

Multiply/Divide the coefficients, then multiply/divide the

radicands (Underneath the root).

5.2 ? Mulitplying and Dividing Radicals(Solutions).notebook

To Multiply:

where:

m, n, a, b are real numbers

Example 1: Simplify the expression

October 19, 2015

5.2 ? Mulitplying and Dividing Radicals(Solutions).notebook

To Divide:

where:

m, n, a, b are real numbers

October 19, 2015

5.2 ? Mulitplying and Dividing Radicals(Solutions).notebook

October 19, 2015

RATIONALIZING DENOMINATORS

Rationalizing ? The process when there is a radical

in the denominator, both the numerator and

denominator must be multiplied by an expression

that will produce a rational denominator.

(ie. Multiply the top and bottom of a fraction to eliminate

the radical on the bottom)

Example 2: Simplify and Rationalize the following expressions.

5.2 ? Mulitplying and Dividing Radicals(Solutions).notebook

c)

d)

October 19, 2015

2¡Ì5

6¡Ì40

If the denominator is a binomial (2 terms), we must

rationalize using it's CONJUGATE.

Conjugates ? 2 binomial factors whose product

is the difference of 2 squares.

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