1-3 Square Roots - Math Slide Show

Lesson 1-3
Objective - To estimate and simplify square
roots.
Radical
symbol
16
Radicand
16 = 4, because 4 • 4 = 16.
4 is the principal root of 16.
Every positive number has two roots.
Positive Square Root Negative Square Root
(Principal Square Root)
16 = 4
− 16 =−4
The square root is not the inverse of a square
because it gives only the positive i root.
Consider the following:
x 2 = 100 x = 100
x = 10 or −10
Two solutions
x = 10
One solution
Between what two whole numbers does the
irrational root lie?
1) 10 3) 104
9 < 10 < 16
3 < 10 < 4
2) 20 4) 57
16 < 20 < 25
4 < 20 < 5
100 < 104 < 121
10 < 104 < 11
49< 57 < 64
7 < 57 < 8
Simplifying Square Root Expressions
a • b = ab
Example: 4 • 9 = 36
2 • 3 = 6
ab = a • b
20 = 4 • 5 = 4 • 5
20 = 2 5
2 • 5 = 2 5
Check using a calculator!
Simplify.
1) 72 3) 8 • 3 = 24
36 • 2 = 6 2 2 6
2) 5 135 4) 2 6• 3 10
5 9•15
2 • 3 6•10
5 • 3 15= 15 15 6 4•15 = 12 15
Simplify.
1)2 12• 7 3) 2 4 • 5 3• 6
2 4• 3• 7
2 • 2 21
4 21
2 • 5 4• 3• 3• 2
10 • 2 • 3 2
60 2
2) 4 2• 5 16 4) 2 6• 8 10• 3 17
4 • 5 2•16 2 • 8 • 3 2• 3• 2 • 5 •17
20 • 4 2
96 3• 5 •17
80 2
96 255
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010

Lesson 1-3 (cont.)
Adding and Subtracting Square Roots
Simplify.
1) 3 7 + 5 7 3) 2 5 + 5 − 7 5
8 7 −4 5
2) 5 3− 3 4) 6 2 − 2 − 2 6
4 3
5 2 − 2 6
Simplify.
1) 12 − 27 3) 75 − 48 + 3
4 • 3 − 9 • 3 25 • 3 − 16 • 3 + 3
2 3− 3 3 =− 3 5 3− 4 3+ 3= 2 3
2) 72 − 8 4) 90 − 40 + 20
36 • 2 − 4 • 2 9 •10 − 4 •10 + 4 • 5
6 2 − 2 2 = 4 2 3 10 − 2 10 + 2 5
10 + 2 5
Three Rules for Simplifying Radical Expressions
1) Leave no perfect square factor in a radical.
50 = 25 • 2 = 25 • 2 = 5 2
1)
Simplify.
5
9
= 5 9 = 5
3
3)
1
6
= 1 ⎛ 6 ⎞
⎜ ⎟
6 ⎝ 6 ⎠ = 6
6
2) Leave no fractions or decimals in a radical.
3
4 = 3
4 = 3
2
3) Leave no radicals in a denominator.
4
3 = 4 3 = 2 ⎛ 3 ⎞
⎜ ⎟ = 2 3
3 ⎝ 3 ⎠ 3
3
3 3
2) = = 4)
2 2
=
12 12
8 8 4 • 2 5 5 = 5
3 ⎛ 2 ⎞ 6
= ⎜ ⎟=
= 4 • 3 = 2 3 ⎛ 5 ⎞
⎜ ⎟
2 2⎝
2 ⎠ 2 • 2 5 5 ⎝ 5 ⎠
= 6
= 2 15
4
5
Simplify.
1) 8 1 = 25 6
= 25 3) 0.06 =
3 3 3
100
= 5 ⎛ 3 ⎞
6
⎜ ⎟= 5 3 =
3
100 = 6
⎝ 3 ⎠ 3
10
3 6⎛
2 ⎞
4 5
2) ⎜ ⎟= 3 12 ⎛ 10 ⎞
4) ⎜ ⎟
2 ⎝ 2 ⎠ 2 10 ⎝ 10 ⎠
= 3 4• 3 = 6 3 = 4 25• 2
2 2
10
= 3 3
= 2 2
= 4 50
10
= 20 2
10
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010