1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write...
-
Upload
sandra-garrett -
Category
Documents
-
view
222 -
download
0
Transcript of 1.1 Square Roots of Perfect Squares Math 90. For each shaded square: –What is its area? –Write...
![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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/1.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/2.jpg)
• 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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/3.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/4.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/5.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/6.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/7.jpg)
• 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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/8.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/9.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/10.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/11.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/12.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/13.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/14.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/15.jpg)
Mr. Pythagoras
• Junior High Math Applet
Remember, we can only use Pythagorean Theorem on RIGHT angle
triangles!
![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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/16.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/17.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/18.jpg)
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.](https://reader036.fdocuments.net/reader036/viewer/2022062300/56649d9d5503460f94a8739f/html5/thumbnails/19.jpg)
Assignment Time!
• Complete the following questions in your notebook.
• Be prepared to discuss your answers in class.
• Show all of your work!