Download Section 1.1 – Square Roots of Perfect Squares

Math 9
Name : __________________________
Date: _____________________
Section 1.1 – Square Roots of Perfect Squares
What is another way of saying a number raised to the power of 2? _______________________
For example, 32 = ___ x ____ = _____. Therefore, we say that 9 is a ______________________
because it can be written as the ____________ of _______ equal numbers.
Here is a picture of the first five whole number perfect squares. You do the 6th one!
12: one squared
22: two squared
32: three squared
Side length = _______
Side length = _______
Side length = _______
Area = __________
Area = __________
Area = __________
42: four squared
52: five squared
Side length = _______
Area = __________
62: ___________________
Side length = _______
Side length = _______
Area = __________
Area = __________
Question: If you know the SIDE LENGTH of a square, how can you calculate its AREA?
Answer: ________________________________________________________________________
Complete the chart to come up with first 25 whole number perfect squares (or area of squares with
whole number side lengths):
Perfect Squares:
1
2
3
4
5
1
4
9
16
25
16
Perfect Squares:
17
18
6
19
7
20
8
21
9
10
22
11
23
12
24
13
14
25
15
etc
...
Example 1: Calculate the area of the following squares with given side lengths.
a)
b
c)
2.1 m
8 cm
3
inch
7
d)
e)
Perfect squares do not need to be a product of just whole numbers. We can find perfect squares
that are rational numbers (. ____________&_____________) as shown in examples 1d and 1e.
Example 2: Draw a picture to show
25
that
is a perfect square.
36
Example 3: Draw a picture to show
that 1.21 is a perfect square.
Example 3: Determine if each of the following rational numbers are perfect squares. Justify your
answer with a picture or words.
c) 0.64
d) 2.25
9
8
a)
b)
16
18
For every mathematical operation, there is an inverse operation - ______________________ .
The inverse of adding is ________________ and the inverse of dividing is ____________________
For squaring, the inverse operation is ______________________________________________ .
Recall that if we know the SIDE LENGTH, we find the AREA by ______________ the side length.
So if we know the AREA, we can find the SIDE LENGTH by doing the inverse operation – or by
____________________________________________.
Example 4: This model shows the number 169 as a square. From the model, state 2 ways of
determining the side length.
Method 1:
Method 2:
Note: From example #5, we can say that ________ is the square root of _____________.
The mathematical notation is _________________________.
Example 5: Calculate the number whose square root is:
3
a)
b) 4.3
c) 0.45
11
Example 7: Determine the side length of the following squares:
a)
b)
Area = 196 mm 2
Area =
25
49
cm 2
c) square with area 0.0361 cm2
CHALLENGE 1: Look at your table of perfect squares on the first page: see that 36, 64 and 100
are related because 36 + 64 = 100. These numbers form a PYTHAGOREAN TRIPLE (related to
Pythagoras’s theorem a2 + b2 = c2. Find other Pythagorean triples. You can go beyond the perfect
squares in the list on the first page!
CHALLENGE 2: French mathematician Pierre de Fermat stated that any whole number can be
written as the sum of four or fewer perfect squares. For example, 21 = 1 + 4 + 16. Try and write
the numbers 33 and 143 as the sum of four or fewer perfect squares.
Assignment: Page 11:
(3, 5, 7) do at least the odd letters;
8, 9, 10, 12, 13, 14, 15 challenge: 18, 19