Section 1.1 Extra Practice Answers
兹5
2 ⫹ 4兹3
兹x ⫹ 2 ⫹ y
2兹7 ⫺ 兹11
兹a ⫺ b ⫹ 兹a ⫹ b
⫺兹u ⫺ v ⫺ 5
2. a.
b.
c.
d.
e.
f.
5
⫺44
x ⫹ 2 ⫺ y2
17
⫺2b
u ⫺ v ⫺ 25
3. If you are given an expression like E1 ⫹ E2, where E1
and E2 are one-term expressions maybe involving a
radical, then its conjugate expression is E1 ⫺ E2.
Multiplying E1 ⫹ E2 by E1 ⫺ E2 will get rid of
radicals, but will create a new expression that is not
equal to the original E1 ⫹ E2. To get around this, we
multiply and divide E1 ⫹ E2 by its conjugate
expression, and get
E1 ⫺ E2
E1 ⫹ E2 ⫽ (E1 ⫹ E2 )
E1 ⫺ E2
2
(E1 ) ⫺ (E2 ) 2
⫽
E1 ⫺ E2
1 ⫺ 兹5
2
b. ⫺1
c. 1 ⫹2 兹5 ⫽ ⫺1 ⫺2 兹5, the negative of the
golden ratio conjugate expression
5. a.
⫽ ⫺1 ⫹2 兹5, the negative of the
golden ratio
e. The golden ratio and its conjugate are the roots of
this equation.
d.
6. a. ⫺3兹5(兹2 ⫹ 兹3)
兹5(兹2 ⫺ 兹3)
b.
15
7(兹2x 2 ⫺ 1 ⫺ 3)
c.
2x 2 ⫺ 10
兹t 7 (2兹t ⫺ 兹2t 2 ⫺ 3t ⫹ 5)
d.
2t 2 ⫺ 7t ⫹ 5
a 8 (2a 3 ⫹ 5兹a)
e.
4a 5 ⫺ 25
兹u 2 ⫺ v 2 (兹u ⫺ v ⫹ u 2 ⫹ v 2 )
f.
(u ⫺ v) ⫺ (u 2 ⫹ v 2 ) 2
This final form is equivalent to the original
expression, and does not involve radicals in the
numerator. This process is called “rationalizing the
numerator”. A similar process exists for rationalizing
an expression in a denominator.
4. a.
b.
c.
d.
e.
f.
324
2
1 ⫺ 兹5
6
兹3(兹5 ⫺ 兹7)
⫺1
兹3(兹5 ⫹ 兹7)
x2 ⫺ 9
4(兹x 2 ⫺ 5 ⫺ 2)
t 2 ⫺ 3t ⫹ 1
兹t 3 (兹t ⫺ 兹t 2 ⫺ 2t ⫹ 1)
a3 ⫺ 1
2a 3 (a 2 ⫹ 兹a)
u ⫺ v ⫺ (u ⫹ v) 2
兹u 2 ⫺ v(兹u ⫺ v ⫹ u ⫹ v)
Calculus and Vectors: Section 1.1 Extra Practice Answers
Copyright © 2009 by Nelson Education Ltd.
1. a.
b.
c.
d.
e.
f.