Squares & Square
Roots
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
146
300
324
729
Activity:
Identify the following numbers
as perfect squares or not.
16 = 4 x 4
ii. 15
iii. 146
iv. 300
v. 324 = 18 x 18
vi. 729 = 27 x 27
i.
Square Numbers
 When you do 4 x 4, you get
16.
4
4
16
 The number 4 is called the
square root of 16, because
that is what is multiplied
twice to get 16.
 We write:
16
=
4
Perfect Square Root
 A number which, when
multiplied by itself, results in
another number.
 Ex: 5 is the square root of 25.
25 = 5
Finding Square Roots
 Activity: Find the square root of 256
256
= 16
Estimating
Square Roots
64 = ?
Estimating
Square Roots
64 = 8
Estimating
Square Roots
49 = ?
Estimating
Square Roots
49 = 7
Estimating
Square Roots
27 = ?
Estimating
Non-Perfect Square Roots
 To calculate the square root of a
non-perfect square
1. See what numbers multiply to give
you the number inside of the
square root symbol.
2. Take the square root of any of
those numbers (if possible).
Estimating
Square Roots
27 = ?
Since 27 is not a perfect square, we
have to use another method to
calculate it’s square root.
Estimating
Non-Perfect Square Roots
Not all numbers are perfect
squares.
Not every number has an Integer
for a square root.
We have to estimate square roots
for numbers between perfect
squares.
Estimating
Non-Perfect Square Roots
 Example:
27
 What two numbers multiply to give you 27?
 Estimate:
27
=
3x9
 Since you can take the square root of 9,
remove that from the inside
3
3
Estimating
Square Roots
32 = ?
Different Versions of
Square Roots
 Negatives
- 49
*take the square root of the
number and keep the negative
sign attached
-7
 Fractions
25
36
*take the square root of the
numerator and denominator and
keep as a fraction
5
6
Different Versions of
Square Roots
 Positive/Negative
+ 36
*take the square root of the
number and keep the
positive/negative sign attached
+6
 Impossible Roots
-16
Since there is no number times
itself equal to -16, there is NO
REAL SQUARE ROOT