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```Warm Up 11/9/2015

Who makes it, has no need of it.
Who buys it, has no use for it.
Who uses it can neither see nor
feel it.
What is it?
A Coffin!!!
Squares & Square
Roots
Perfect Squares
Square Number
 Also called a “perfect square”
 A number that is the square of a
whole number
 Can be represented by
arranging objects in a square.
Square Numbers
Square Numbers
1x1=1
2x2=4
3x3=9
 4 x 4 = 16
Square Numbers
1x1=1
2x2=4
3x3=9
 4 x 4 = 16
Activity:
Calculate the perfect
squares up to 152…
Square Numbers
1x1=1
 9 x 9 = 81
2x2=4
 10 x 10 = 100
3x3=9
 11 x 11 = 121
 4 x 4 = 16
 12 x 12 = 144
 5 x 5 = 25
 13 x 13 = 169
 6 x 6 = 36
 14 x 14 = 196
 7 x 7 = 49
 15 x 15 = 225
 8 x 8 = 64
Activity:
Identify the following numbers
as perfect squares or not.
i.
ii.
iii.
iv.
v.
vi.
16
15
21
36
64
71
Activity:
Identify the following numbers
as perfect squares or not.
16 = 4 x 4
ii. 15
iii. 21
iv. 36 = 6 x 6
v. 64 = 8 x 8
vi. 71
i.
Squares &
Square Roots
Square Roots
Finding a root of a number is the inverse operation of
raising a number to a power.
index
n
a
The index defines the root to be taken.
Square Root
 A number which, when
multiplied by itself, results in
another number.
 Ex: 5 is the square root of 25.
5 =
25
Every positive number has two square
roots, one positive and one negative

 When you calculate the
square root of a number
on a calculator, only the
positive square root
appears. This is the
principal square root.
 Principal Square RootThe non-negative
square root of a
number.
Activity:
Find the principal square roots
of the following numbers

Warm Up 11/10/15

What gets wetter and
wetter the more it
dries?
A towel!!!
a b
ab
ONLY when a≥0 and b≥0
For Example:
9  16  9 16  144  12
9  16  3  4  12
Equal
Simplify the following
expressions

Simplifying Square Roots
Write the following as a radical (square root) in simplest
form:
36 is the biggest perfect square that divides 72.
Simplify.
72  36  2  36 2  6 2
Rewrite the square root as a product of roots.
27  9  3  9 3  3 3
Ignore the 5 multiplication until the end.
5 32
 5 16  2  5 16 2  5  4  2
 20 2
Simplifying Square Roots
A) 16
4
B) 8
C) 7
E )4 63  12
2 2
D) 75
7
5 3
F ) 128  8
2
11/12/15 Warm up

A man is pushing his
car along, and when
he reaches a hotel he
shouts “I’m
bankrupt!” Why?
He’s playing
Monopoly!!!
a

b
a
b
ONLY when a≥0 and b≥0
For Example:
64
16
64
16

64
16

 4 2
8
4
2
Equal
Simplify the expressions

Simplifying Radicals using the Quotient Rule
Quotient Rule for Square Roots
If
a and b are real numbers and b  0, then
Examples:
16 4
16


81
81 9
45

49
45

49
2

25
95 3 5

7
7
2
2

5
25
a
a

b
b
The Square Root of a Fraction
Write the following as a radical (square root) in simplest
form:
Take the square root of the numerator and the denominator
3
3
3


2
4
4
Simplify.
Simplify the expressions

Warm Up 11/13/15
Define the following (you can look
these up on your computer if you
don’t know them!):
Rational Number any # that can be expressed as the
quotient of 2 integers
Irrational Numberany real # that cannot be expressed as
a ratio of integers.
What can run but
never walks, has a
mouth but never
talks, has a bed but
never sleeps?
A river!!!!
Rationalizing a Denominator
The denominator of a fraction cannot contain a radical.
To rationalize the denominator (rewriting a fraction
so the bottom is a rational number) multiply by the
Simplify the following expressions:
5 2
5 2
5
2



2
2
2 2
2
 
6 3 6 3 3 2 3 2 3
6 3
3






2
35
5
15
53
3 5 3
5 3
6
 
Why do we rationalize the
denominator?
 The main reason we do this is to have a
standard form in which certain kinds of
answers can be written. That makes it
easier for us as teachers to check answers,
and for the students to check their own