Perfect Squares and Square Roots
Write all the perfect squares from 1 to 400 in the following manner:
1 x 1 = 1² = 1 (perfect square)
2 x 2 = 2² = 4 (perfect square)
Look at your completed work. See the pattern? Complete the pattern
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400
3 5 7 9 11 13
Now calculate the differences once again. What is the final pattern?
In your notebooks, create and complete the following Perfect Square table
for squares 1, 4, 9, 16, 25, 36, 49
Perfect Sq
PSq Figure
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Square Root Process
Square Root
1
1
___
_______
√ 1 = √ 1 x 1
=
1
(measure of a side)
4
2
2
___
_______
√ 4 = √ 2 x 2
=
2
(measure of a side)
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Let’s look at two important distinctions with squares:
A)
12, 2², 3², 4², 5², 6², 7², etc… are in computation form. Each is
written as one squared, two squared, three squared, four squared, etc. Each
is solved in the following manner:
1 x 1 = 2 x 2=
3 x 3=
4 x 4=
5 x 5=
6 x 6=
7 x 7=
Or
on your calculator, key the base number, key the x² button and view the
answer.
B)
When you are asked to sketch a one square, four square, nine square, sixteen
square, twenty five square etc… you sketch a one square (1x1), a four
square (2x2), a nine square (3x3), etc. These are not the same as in A
above.
1. Using grid paper, show the square root of 36, 49, 81.
2. Using grid paper, show all perfect squares less than 100.
3. Use square roots to solve: A square has an area of 81m². What are its
dimensions?
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Challenge: A cube has a surface area of 294m². What are its dimensions?
Textbook:
Page 42: Let’s discuss CD together.
Now, from UA on pages 42-43, do
1ac 2 4 5
6 7 8 11
12 13 and
In Your Journal
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Learners are to show all work in Math. Here is one
example why they must do so:
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The square on the left has a measure of 4 units on each side. Add the
measures around and the total is 16. The square is 16. This answer is
correct. However, the method used is for determining Perimeter not
Squares!
Look at the square on the right.
Using the student rational from above, the square must be 12. Is this answer
correct? Absolutely not!
Showing your work:
If, for example, a square has a measure of 3 units on one of its sides, then a
learner can prove the square to be 9 not 12 by showing work. Do this by
extending the divisions three across, three down and discovering the figure
to have 9 squares not 12.
Getting the answer “right” does not always mean that you understand the
concept.
By showing your work, you not only show your answer to be correct,
but you also prove that you understand the concept.
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