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Name
Class
Date
Reteaching
5-6
Simplifying Radicals
You can remove perfect-square factors from a radicand.
Problem
What is the simplified form of 80n5 ?
In the radicand, factor the coefficient and the variable separately into perfect
square factors, and then simplify. Factor 80 and n5 completely and then find
paired factors.
Solve
Factor 80 completely.
80 = 8 · 10 = 2 · 2 · 2 · 2 · 5
= (2 · 2)(2 · 2) · 5 = (2 · 2)2 · 5
ab = a  b.
The square root of a number squared
is the number: a2 = a.
80  42 · 5  42  5
Use the rule
 4 5  4 5
n5 = n · n · n · n · n
Factor n5 completely.
= (n · n) · (n · n) · n = (n · n)2 · n
n  (n  n)  n
5
2
 n  n  n
2
2
n
80n5
4n2 5n
80n5
4 n 2 5n
Remove the perfect square.
Combine your answers.
Check your solution.
Divide both sides by
5n
5n
Find pairs of factors.
Separate the factors.
80n5  4  n2 (5  n)2  4n2 5n
Check
Find pairs of factors.
16n4 = 4n2
Simplify.
4n2 = 4n2
Solution: The simplified form of 80n5 is 4n2 5n .
Exercises
Simplify each radical expression.
1.
100n3
2.
120b4
3.
66t 5
4.
32x
5.
525c7
6.
86t 2
7.
50g 3
8.
54h6
9.
35y
Pearson Texas Algebra I
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
5n .
Name
Class
Date
Reteaching (continued)
5-6
Simplifying Radicals
Problem
27t 4
?
48t 2
What is the simplified form of
Begin by cancelling the common factors in the numerator and denominator. Simplify
the numerator and denominator separately when the denominator is a perfect square.
Remember that the radical is not simplified if there is a radical in the denominator.
Multiply to remove the radical from the denominator.
Factor the numerator and denominator
27t 4
333t t t

2
3
44tttt
48t
Solve
completely.
=
=
=
Cancel the common factors.
(3  3)
(4  4)t
32

Find pairs of factors. These are the perfect-
2
square factors.
4 t
3
Simplify the numerator and denominator
4 t
separately to remove the perfect-square
factors.
=
=
t to remove
4 t ( t)
4 t t

42 t = 4 t
Multiply the numerator and denominator by
3 ( t)
3 t
32  3 and
3 t
4 t2

t from the denominator.
Remove the perfect-square factor from the
3 t
4t
denominator.
27t 3 3 t
is
.
4t
48t 4
Solution: The simplified form of
Exercises
Simplify each radical expression.
10.
49
81
11.
18 x 4
200
12.
28s
s3
13.
25a 5
9a 7
14.
40b 4
12b 3
15.
48
6b 6
16.
50 z 3
4a 2
17.
t5
64
18.
32t
t
Pearson Texas Algebra I
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.