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Math 9
2.4 Notes
The ________ ________ of a number is one or more equal factors of that number
(Or you can think of a square root of a number as being the factor you have to
square in order to get the original number)
 I.e.
16 = 4x4 = 42 so we say 4 is the square root of 16
A __________ square is a number who can be expressed as a product of two
equal rational factors.
 I.e.
9 = 3x3 = 32
since we know 3 is the square root of 9 and 3 is a
rational number, then we know 9 is a perfect s
square.
A _____-___________ square is a number that cannot be expressed as a product
of two equal rational factors.
 I.e.
3 = (1.732…)x(1.732…) = (1.732…)2 since (1.732…) is not a rational
number, we conclude that 3 is a
non-perfect square.
****An important fact about non-perfect squares is that their factors are
IRRATIONAL. (Why is this?)****
Math 9
• Another way to think about perfect squares is in terms of an area
 How would we represent the following numbers?
4
1
16
25
0.16
0.25
What about 17?
Math 9
On your Own:
List the perfect squares associated with the square roots 1-12:
Square Root
Perfect Square
1
2
3
4
5
6
7
8
9
10
11
12
***You should KNOW these values***
Determining Whether a Fraction is a Perfect Square:
In order for a fraction to be a perfect square, both the numerator and
denominator must be perfect squares
I.e.
4
9
9
25
4
16
Math 9
On your Own:
Are the following rational numbers perfect squares?
a)
1
b)
25
c)
4
9
16
10
d) 1
7
9
Determining Whether a Decimal is a Perfect Square:
Steps:
1. Convert the decimal to a fraction
2. Determine whether the numerator and denominator are perfect squares
Example:
Is 0.64 a perfect square?
On your Own:
Determine whether the following rational numbers are perfect squares:
a) 0.81
Math 9
b) 0.22
c) 1.44
Determining a Rational Number from a non-Perfect square root:
If you are asked to find the square of a number that is not a whole number what
do you do?
1. Estimate:
a. Round it to the closest whole number above and below
b. Determine how close your number is to the nearest whole number
c. Estimate the answer
2. Calculate (punch the number in your calculator)
Example:
Stevie bought a new square trampoline that measures 2.6m by 2.6m. How much
area will his trampoline cover?
a) Estimate:
b) Calculate:
Math 9
Estimating the Square Root of a non-Perfect Square:
We follow the same process when we want to estimate the square root:
Example:
Estimate then calculate the following square roots of
a) 73
b) 0.22
Assignment: 1-6, 7, 9, 11, 15, 16 (p. 78-80)