1. Square Roots of Non-Perfect Squares
Math 8

2. 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?

3. Here are 2 strategies...
Ask yourself: “Which 2 perfect squares are closest to 7.5?”
7.5 2 3
2.5
7.5 is closer to 9 than to 4, so is closer to 3 than to 2.
What would be a good approximation?

4. Strategy #2... Use a calculator! 
But, of course, you must be able to do both!

5. We call these 2 numbers ‘benchmarks’.
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?

6. Of course, you can always use a calculator to CHECK your answer!
Example #2
Determine an approximate value of each square root.
Your benchmarks!
0.40
0.30
0.20
0.25
0.36
Of course, you can always use a calculator to CHECK your answer!

7. If these are the square roots, where do we start?
What’s 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
100
110
120 or 10 11

8. Recall: a2 + b2 = c2 Mr. Pythagoras Junior High Math Applet
Remember, we can only use Pythagorean Theorem on RIGHT angle triangles!

9. 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

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

11. 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?

12. Assignment Time! Complete the following questions in your notebook.
Be prepared to discuss your answers in class.
Show all of your work!
Write this assigned questions on your assignment sheet:
Pg. 18/19: 4ae, 5ab, 6ab, 7bc, 8ab, 9ab, 10ac, 11bef, 13ac