Section 1.1 Extra Practice
STUDENT BOOK PAGES 6–9
1. Determine the conjugate of each expression.
a. 兹5
b. 2 ⫺ 4兹3
c. 兹x ⫹ 2 ⫺ y
d. 2兹7 ⫹ 兹11
e. 兹a ⫺ b ⫺ 兹a ⫹ b
f. ⫺兹u ⫺ v ⫹ 5
2. For each part in problem 1, after multiplying by the
appropriate conjugate expression give the resulting
simplified expression. (Note: This resulting
expression will not involve radicals, but will not be
equivalent to the original expression.)
3. Describe, in your own words, the process of
rationalizing a non-fractional expression. Be sure to
describe what must be done to ensure that the
resulting expression is equivalent to the original one.
4. Rationalize the numerator of each of the following
expressions, and give the simplified equivalent
expression.
Copyright © 2009 by Nelson Education Ltd.
a.
b.
c.
d.
e.
f.
2兹3
兹5 ⫺ 兹7
兹5 ⫺ 兹7
5. The number 1 ⫹2 兹5 is known as the golden ratio,
and shows up in various natural situations.
The ancient Greeks used this number as a guide in
their architectural designs for the ratio of width to
height for building fronts (so the width
would be 1 ⫹2 兹5 times the height for the front of
the building).
a. What is the conjugate expression for the golden
ratio?
b. What do you get if you multiply the golden ratio
by its conjugate?
c. Rationalize the denominator of the reciprocal of
the golden ratio. What do you notice?
d. Repeat part c. for the conjugate of the golden
ratio.
e. Can you find a connection between the golden
ratio, its conjugate expression, and the algebraic
equation x 2 ⫺ x ⫺ 1 ⫽ 0?
6. Rationalize the denominator of each of the following
expressions and give the simplified equivalent
expression.
3兹5
a.
兹2 ⫺ 兹3
b.
2兹3
兹x 2 ⫺ 5 ⫹ 2
4
c.
⫺兹t 2 ⫺ 2t ⫹ 1 ⫺ 兹t
d.
兹t 3
a 2 ⫺ 兹a
e.
2a 4
兹u ⫺ v ⫺ u ⫺ v
f.
兹u 2 ⫺ v
兹2 ⫺ 兹3
3兹5
7
兹2x 2 ⫺ 1 ⫹ 3
兹t 7
⫺兹2t 2 ⫺ 3t ⫹ 5 ⫺ 2兹t
a9
2a 3 ⫺ 5兹a
兹u 2 ⫺ v 2
兹u ⫺ v ⫺ u 2 ⫺ v 2
Section 1.1 Extra Practice
323