1.1 Square Roots of Perfect Squares

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1.1 Square Roots of Perfect Squares

• Math 90

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• 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?

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Calculate the Area
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Calculate the side length
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For the area of each square in the table

• Write the area as a product.
• Write the side length as a square root.

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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.

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• When you take the square root of other fractions
  you will get a repeating decimal.
• Eg.
• These are all called RATIONAL numbers

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1.2 Square Roots of Non-Perfect Squares

• d

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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?

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Here are 2 strategies...
Ask yourself Which 2 perfect squares are
closest to 7.5?
7.5
7.5 is closer to 9 than to 4, so is closer to 3
than to 2.
What would be a good approximation?
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Strategy 2...

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

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Example 1

• Determine an approximate value of each square
  root.

We call these 2 numbers benchmarks.
close to 9
close to 4
What does this mean?
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Example 2

• Determine an approximate value of each square
  root.

Your benchmarks!
0.36
0.25
Of course, you can always use a calculator to
CHECK your answer!
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Whats the number?

• Identify a decimal that has a square root between
  10 and 11.

If these are the square roots, where do we start?
121
110
100
120
or
10
11
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Mr. Pythagoras
Recall a2 b2 c2

• Junior High Math Applet

Remember, we can only use Pythagorean Theorem on
RIGHT angle triangles!
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Practicing the Pythagorean Theorem
First, ESTIMATE each missing side and then CHECK
using your calculator.
7 cm
x
13 cm
5 cm
8 cm
x
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Applying the Pythagorean Theorem
1.5 cm
2.2 cm
6.5 cm
The sloping face of this ramp needs to be covered
with Astroturf.

1. Estimate the length of the ramp to the nearest
   10th of a metre
2. Use a calculator to check your answer.
3. Calculate the area of Astroturf needed.

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Lets quickly review what weve 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?

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Assignment Time!

• Complete the following questions in your
  notebook.
• Be prepared to discuss your answers in class.
• Show all of your work!