# 1.2 Square Roots of Non-Perfect Squares by rt3463df

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```									1.2 Square Roots of
Non-Perfect Squares
Math 90
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?
Here are 2 strategies...
perfect squares are                7.5
closest to 7.5?”
7.5

2           2.5           3

7.5 is closer to 9 than to 4, so 7.5 is closer to 3 than to 2.
What would be a good approximation?
Strategy #2...
• Use a calculator! 
• But, of course, you must be able to do
both!
Example #1
• Determine an approximate value of
each square root.
8      close to 9    We call these 2
numbers
5      close to 4    „benchmarks‟.

8 3

5 2

What does this
mean?
Example #2
• Determine an approximate value of
each square root.
Your
3
 0.3   benchmarks!
10

0.20   0.25     0.30     0.36 0.40

3                 Of course, you can always
 0.55          use a calculator to CHECK
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

10                       11
Mr. Pythagoras

• Junior High Math Applet

Remember, we
can only use
Pythagorean
Theorem on
RIGHT angle
triangles!
Practicing the Pythagorean
Theorem
First, ESTIMATE each missing side and then

7 cm

x                  13 cm
5 cm

8 cm
x
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.

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

c) Calculate the area of Astroturf needed.
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?
Assignment Time!
•   Complete the following questions in your notebook.