Transcript Squares & Square Roots

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 Roots
Square Numbers
One property of a perfect
square is that it can be
represented by a square array.
4 cm
4 cm
16 cm2
Square Numbers
The large square has an area of 4cm x 4cm = 16 cm2.
The number 4 is called the square root of 16.
4cm
4cm
16 cm2
We write: 16 = 4
We say: The square root of 16 is 4
or “radical 16” is 4
Square Root
A number which, when multiplied by
itself, results in another number.
Ex: 5 is the square root of 25.
25 = 5
Simplifying Square Roots
We can use the following strategy to simplfy
square roots
125
=
25 x 5
125
=
5 x 5
125
= 5 5
Break the
number into a
product where
one of the
factors is a
perfect square
Simplifying Square Roots
Simplify:
200
=
100 x 2
= 10 x 2
= 10 2
Simplifying Square Roots
Simplify:
80
=
16 x 5
=4x 5
= 4 5
Simplifying Square Roots
Simplify:
75 + 48
25 x 3 + 16 x 3
5x 3 +4x 3
5 3 +
4 3
9 3
Estimating
Square Root
Estimating 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 Square Roots
25 = 5
36 = 6
27 = ?
Since 27 is not a perfect square, we
have to use another method to
calculate it’s square root.
Estimating Square Roots
Example:
27
What are the perfect squares on each side of 27?
5
6
25
25
30
27
Estimate
35 36
27 = 5.2
Estimating Square Roots
Estimate:
27
= 5.2
Check: (5.2) (5.2) = 27.04
Estimating Square Roots
Example:
6
What are the perfect squares on each side of 7?
3
2
0
4
5
9
10
6
Estimate
6 = 2.4
Estimating Square Roots
Estimate:
6
= 2.4
Check: (2.4) (2.4) = 5.76
Estimating Square Roots
Example:
56
What are the perfect squares on each side of 56?
8
7
49
50
55
60
56
Estimate
56 = 7.5
65
64
Estimating Square Roots
Estimate:
56
= 7.5
Check: (7.5) (7.5) = 56.25