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


Side length = ______

Area = ______/ 22: two squared



Side length = ______

Area = ______/
32: three squared
Side length = ______

Area = ______
42: four squared

Side length = ______

Area = ______/ 52: five squared
Side length = ______

Area = ______/ 62: ______
Side length = ______
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):

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15
Perfect Squares: / 1 / 4 / 9 / 16 / 25
16 / 17 / 18 / 19 / 20 / 21 / 22 / 23 / 24 / 25 / etc
Perfect Squares: / / / / ...

Example 1: Calculate the area of the following squares with given side lengths.

a)


/ b / c)
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 Example 3: Draw a picture to show

that is a perfect square. 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.

a) / b) / c) 0.64 / d)

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.

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:

a) b) c) 0.45

Example 7: Determine the side length of the following squares:

a) b) 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