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7-2 MULTIPLYING AND DIVIDING RADICAL EXPRESSIONS (p. 368-373)
Multiplying Radical Expressions
If n a and n b are real numbers, then n a  n b  n ab (The product of the
principal n th roots of two numbers equals the principal n th root of their product).
For instance,
9  25  9  25
3  5  225
15 =15
Also,
3
 125  3 8  3  125  8
 5  2  3  1000
 10  10
Example: Multiply. Simplify if possible.
1. 3  12
2. 3  16  3 4
3.  4  16
Do 1 b and c on p. 368.
When simplifying radical expressions, look for perfect squares, perfect cubes, etc. that
are factors of the radicand (depending on what n is).
Example: Simplify each expression. Assume all variables are positive (therefore, no
absolute value symbols are needed in the answer).
50x 5
1.
2.
3
54n 8
3.
4
32x11
Do 2 on p. 369.
You can also simplify products of radicals.
Example: Multiply and simplify. Assume all variables are positive.
3
25xy 8  3 5x 4 y 3
Do 3 on p. 369.
Dividing Radical Expressions
If
n
principal n th
n
a
(The quotient of the
b
b
roots of two numbers equals the principal n th root of their quotient).
a and n b are real numbers and b  0, then
n
a
n
Example: Divide and simplify. Assume all variables are positive.
3
 81
1. 3
3
3
2.
384 x 8
3
3x
Do 4 a-c on p. 370.
To rationalize a denominator means to rewrite it so there are no radicals in any
denominator and no denominators (fractions) in any radical.
The book shows two methods to rationalize a denominator. Their method 2 may be
quicker.
Example: Rationalize the denominator of each expression. Assume all variables are
positive.
3
1.
(Show both methods)
5
x5
2.
3.
3x 2 y
3
5
4y
Do 5 b and c on p. 370.
Example: The distance d in meters that an object will fall in t seconds is given by
d  4.9t 2 . Express t in terms of d and rationalize the denominator. In this problem, you
will need to multiply the denominator not by itself, but by another number to get a perfect
square (and eliminate the fraction under the radical).
Do 6 on p. 371.
Homework
p. 371-373: 1,7,9,15,19,21,25,26,29,33,35,43,49,53,57,69,72,73,80,81,85,95
21. 3 3 5y 3  2 3 50y 4  6 3 250y 7  30 y 2
3
2y