Algebra 2 B
Chapter 7
Section 4
nth Roots
Radical sign
index
50
n
radicand
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Simplify Roots
2
5
4
144 x y
2
10
243a b
4a
2
21
15
2
12 x y
=
=
=
2
3a b
3
2a10 a
1
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Simplify Roots
3
12
2
625r g
2
=
2
4
4
Why?
16
=
25 r g
=
3x 1
(3x 1) 2
2
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Simplify Roots
6
x
2
3
(m 4)6
=
m 4
12 x 36 = x 6
27a b = 3a b
9
3
12
4
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Simplify Roots
64 x
25
6
=
8x
5
3
2
Review
By definition 25 is the number you would multiply
times itself to get 25 for an answer.
Because we are familiar with multiplication, we
know that 25 = 5
Numbers like 25, which have whole numbers for their
square roots, are called perfect squares
You need to memorize at least the first 15 perfect
squares
Perfect
square
Square
root
Perfect
square
Square
root
1
1 = 1
81
4
4 = 2
100
100 = 10
9
9 = 3
121
121 = 11
16
16 = 4
144
144 = 12
25
25 = 5
169
169 = 13
36
36 = 6
196
196 = 14
49
49 = 7
225
225 = 15
64
64 = 8
81
= 9
3
Every whole number has a square root
Most numbers are not perfect squares, and so their
square roots are not whole numbers.
Most numbers that are not perfect squares have
square roots that are irrational numbers
Irrational numbers can be represented by decimals
that do not terminate and do not repeat
The decimal approximations of whole numbers can be
determined using a calculator
Obj: To find the square root of a number
• Find the square roots of the given numbers
• If the number is not a perfect square, use a
calculator to find the answer correct to the
nearest thousandth.
81
81 = 9
37
37
158
158
6.083
12.570
Obj: To find the square root of a number
• Find two consecutive whole numbers that the
given square root is between
• Try to do this without using the table
18
16 = 4 and
25 = 5
so
18 is between 4 and 5
115
100 = 10 and
121 = 11
so
115 is between 10 and 11
4
Multiplying radicals
The product of the square roots of two numbers is the same as the square root of the
product of the numbers
Examples:
3
12
=
36
7
11
=
77
Simplify the following expressions
=
- 4
-2
=
7 64 + 9
7 8+9
=
5 25 +
56 + 9
=
49
= 65
5 5+7
=
25 + 7 = 32
Simplify the following expressions
4
81
1
36
=
–
4
81
2
9
=
1
144
=
1
–
=
2
12
1
12
6
–
1
12
1
=
12
5
Simplified radical form
No factor inside the radical should be a perfect square.
18
=
9 2
=
108
=
36 3
=
36 3
=
6 3
96
=
16 6
=
16 6
=
4 6
9 2
=
3 2
6