# Objectives: Work with n th Roots Simplify Radicals A.9 DAY 2

```A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
A.9 DAY 2
n th Roots
Rational Exponents
Objectives:
Work with n th Roots
Jan 21&shy;1:37 PM
1
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Warm‐up
List the squares and cubes of the numbers 1‐10.
12 = 22 = 32 = 42 = 52 = 62 = 72 = 82 = 92 = 102 = 13 = 23 = 33 = 43 = 53 = 63 = 73 = 83 = 93 = 103 =
Nov 3&shy;7:32 AM
2
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Roots
A radical sign is used to indicate a root.
The index gives the degree of the root.
The number under the radical sign is the radicand.
Jan 21&shy;2:32 PM
3
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Roots
Every positive real number has two square roots,
one positive and one negative.
For example: The two square roots of 49 are 7 and ‐7.
The positive square root is also known as the
principal square root
and is denoted with a radical sign: √49 = 7.
Jan 21&shy;2:32 PM
4
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Even Roots
n
√an = |a| if n is even and n ≥ 2.
Simplify each expression.
1. √25
2. √81
3.
√-100
Jan 23&shy;1:58 PM
5
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Roots
Every real number has exactly one cube root.
For example:
3
√8 = 2
AND
3
‐8 = ‐2
√
Jan 21&shy;2:32 PM
6
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Odd Roots
√an = a if n is odd and n ≥ 3.
n
Simplify each expression.
1. ∛27
2. ∛-8
16
3. ∛&shy; 125
Jan 23&shy;1:58 PM
7
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Jan 23&shy;2:10 PM
8
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Example: Simplify each expression. Assume that all variables are positive. a. √72x3
b. ∛80n5
c. √50x4
d. ∛18x4
Jan 19&shy;1:24 PM
9
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Example: Multiply. Simplify if possible.
a. √2 √8
b. ∛&shy;5 ∛25
c. √-2 √8
d. √3 √12
e. ∛3 ∛&shy;9
f. ∜4 ∜&shy;4
Jan 19&shy;1:23 PM
10
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Example: Multiply and simplify. Assume that all variables are positive.
a. ∛54x y ∛5x y
2 3
3 4
b.
3√7x3 2√21x3y2
∛270x5y7 ∛27x3y6 10x2y 3xy2∛10x2y
Jan 19&shy;1:25 PM
11
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
Example: September 22, 2010
Divide and simplify. Assume that all varaibles are positive.
a. ∛32 32
= 3
=
∛&shy;4 &shy;4 ∛&shy;8 = &shy;2 √
b. ∛162x5 162x5 = 3
= ∛54x3 = ∛27x3(2) = 3x∛2
2
2
∛3x 3x √
Jan 6&shy;10:52 AM
12
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Like radicals are radical expressions that have the same index and the same radicand. We can add and subtract like radicals.
Add or subtract if possible.
a. 5∛x - 3∛x
b. 4√2 + 5√3
d. 7∜5 - 2∛5
c. 2√7 + 3√7
e. 4√xy + 5√xy
Jan 24&shy;1:11 PM
13
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Simplifying Before Adding or Subtracting
a.
6√18 + 4√8 - 3√72
b.
√50 + 3√32 - 5√18
Jan 24&shy;1:18 PM
14
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
You can multiply radical expressions that are in the form of binomials by using FOIL.
Simplify each expression by multiplying.
b. (√2 - √3)2
a. (3 + 2√5)(2 + 4√5)
Jan 24&shy;1:53 PM
15
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
September 22, 2010
Homework:
page 1037
(7 &shy; 16,
19 &shy; 22,
25 &shy; 31)
Jan 23&shy;2:10 PM
16
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