Math 154 — Rodriguez
Angel — 9.4
Dividing Square Roots
I. Simplifying Quotients
A square root expression is simplified when:
1. No radicand has a perfect square.
2. No radicand contains a fraction.
3. No denominator contains a square root.
Quotient Rule for Square Roots states: if a≥0 and b>0,
a
b
=
Examples: Simplify.
1)
3)
5)
20x 2 y 3
80x 4 y
66x 3
22xy 6
3x 5 y
27xy 3
2)
4)
6)
24m9
25m3 n 4
16x 5 y 3
25xy 3
48x 3
2xy 4
a
b
II. Rationalizing the Denominator
How do we simplify an expression like
1
? Unlike the previous problems, the
3
denominator does not simplify to be a perfect square. We ‘fix’ the denominator by making
it a perfect square. The process is called ‘rationalizing the denominator’ because we are
changing the denominator from an irrational number to a rational number.
To simplify: multiply the numerator and denominator by the square root containing the
factor that would make the radicand in the denominator a perfect square.
Example: Simplify. (NOTE: these have same instructions as the previous problems. In
some textbooks the instructions for these would be ‘rationalize the denominator’.)
1)
1
3
2)
3)
You are thinking: what would make the denominator, the 3, a perfect square?
5
6
3
18
4)
3
8
5)
5
50
6)
Angel — 9.4
7
12
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