Transcript Squares & Square Roots

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
Parts of a Radical Expression
Finding a root of a number is the inverse operation of
raising a number to a power.
radical sign
index
n
a
radicand
This symbol is the radical or the radical sign
The expression under the radical sign is the radicand.
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!!!
Radical Product Property
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
Warm Up 11/12/15
Simplify these radicals:
A) 16
4
B) 8
C) 7
E )4 63  12
2 2
D) 75
7
5 3
F ) 128  8
2
Warm Up Part 2 11/12/15

A man is pushing his
car along, and when
he reaches a hotel he
shouts “I’m
bankrupt!” Why?
He’s playing
Monopoly!!!
Radical Quotient Property
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

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 real # 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
same radical.
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
answers in their book.
 More answers at:
http://mathforum.org/library/drmath/view/5
2663.html
Simplify the expressions
