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1.1 Square Roots of Perfect Squares Math 90

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Page 1: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

1.1 Square Roots of Perfect Squares

Math 90

Page 2: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

• For each shaded square:– What is its area?– Write this area as a product.– How can you use a square root to relate

the side length and area?

Page 3: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Calculate the Area:

Page 4: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Calculate the side length

Page 5: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

For the area of each square in the table…• Write the area as a product.• Write the side length as a square root.

Page 6: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Squaring vs. Square Rooting• Squaring and square rooting are opposite, or inverse

operations.– Eg.

• When you take the square root of some fractions you will get a terminating decimal.

– Eg.

• These are all called RATIONAL numbers.

225

100

29 81 9 3

Page 7: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

• When you take the square root of other fractions you will get a repeating decimal.– Eg.

• These are all called RATIONAL numbers

1

91 1

0.339

Page 8: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

1.2 Square Roots of Non-Perfect Squares

d

Page 9: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Introduction...

• Many fractions and decimals are not perfect squares.

• A fraction or decimal that is not a perfect square is called a non-perfect square.– The square roots of these numbers do not

work out evenly!

• How can we estimate a square root of a decimal that is a non-perfect square?

Page 10: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Here are 2 strategies...

7.5

7.5

Ask yourself: “Which 2 perfect squares are

closest to 7.5?”

2 32.5

7.5 is closer to 9 than to 4, so is closer to 3 than to 2.

7.5

What would be a good approximation?

Page 11: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Strategy #2...

• Use a calculator! • But, of course, you must be able to do

both!

Page 12: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Example #1

• Determine an approximate value of each square root.

8

5close to 9

close to 4

8 3

5 2

What does this mean?

We call these 2 numbers

‘benchmarks’.

Page 13: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Example #2

• Determine an approximate value of each square root.

3

10

30.55

10

0.3

0.25 0.400.300.20 0.36

Of course, you can always use a calculator to CHECK

your answer!

Your benchmarks!

Page 14: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

What’s the number?• Identify a decimal that has a square root

between 10 and 11.

120110100

If these are the square roots, where do we start?

121

1110

Page 15: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Mr. Pythagoras

• Junior High Math Applet

Remember, we can only use Pythagorean Theorem on RIGHT angle

triangles!

http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.PYTH&lesson=html/video_interactives/pythagoras/pythagorasInteractive.html
Page 16: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Practicing the Pythagorean Theorem

5 cm

First, ESTIMATE each missing side and then CHECK using your calculator.

8 cm

13 cm

7 cm

x

x

Page 17: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Applying the Pythagorean Theorem

The sloping face of this ramp needs to be covered with Astroturf.

a) Estimate the length of the ramp to the nearest 10th of a metre

b) Use a calculator to check your answer.

c) Calculate the area of Astroturf needed.

2.2 cm

6.5 cm

1.5 cm

Page 18: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Let’s quickly review what we’ve learned today...

• Explain the term non-perfect square.

• Name 3 perfect squares and 3 non-perfect squares between the numbers 0 and 10.

• Why might the square root shown on a calculator be an approximation?

Page 19: 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write this area as a product. –How can you use a square root

Assignment Time!

• Complete the following questions in your notebook.

• Be prepared to discuss your answers in class.

• Show all of your work!


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The Land Ukraine has an area of 233,089 square miles and 603,700 square kilometers. Ukraine has an area of 233,089 square miles and 603,700 square kilometers

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