Download 7.4 Adding, Subtracting and Dividing Radicals

Math 152 — Rodriguez
Adding, Subtracting, and Dividing Radical Expressions
Blitzer — 7.4
In this section, assume that all variables represent positive real numbers.
I. Adding and Subtracting Radical Expressions
A. To add or subtract terms with radicals we have to combine like terms, in this case, like
radicals.
B. Like radicals are radicals that have the ____________________________ and the
_________________________. You may need to simplify terms to identify like radicals.
Examples: Add or subtract as indicated. You may need to simplify terms to identify like radicals.
1)
2) 114 13x ! 20 4 13x
23 5 + 43 5
3) 9 4 8 + 6 4 8x
4) 5 12 + 2 27
5) 5 3x 3 + 12x
6) 6 3 54 + 8 3 16
7) 3 24x 3 ! 2x 3 81
II. Dividing Radical Expressions
A. To simplify the radical expressions in this section we use the Quotient Rule for Radicals.
n
a na
=
b nb
b ≠ 0,
n
a and
n
b are real numbers
B. A radical expression is simplified when:
1. The radicand does not contain any perfect nth powers.
2. The denominator does not contain a radical.
3. The radicand does not contain a fraction.
Examples: Simplify using the quotient rule.
1)
72x 5
25y 4
3)
3
64x11
27y 9
2)
4
4)
5
32x11
81y 8
64x11
y 30
III. Dividing Radical Expressions
A. To divide radicals we use the Quotient Rule in the “reverse” order.
n
n
a na
=
b
b
Examples: Divide and if possible, simplify.
1)
3)
3
54x 4
3
2x
500x 3 y 2
10x !2 y ! 4
Blitzer — 7.4
2)
4)
4
243x11 y 2
4
3x 2 y ! 5
3 120x 7 y
3
3x 3 y !2
Page 2 of 2