Problem of the Day Bell Work - Plain Local

045 Squares and Square Roots.notebook October 15, 2013

A Shakespearean sonnet is a poem made up of 3 quatrains (4 lines each) and a couplet (2 lines). Each line is in iambic pentameter (which means it has 5 iambic feet). So how many iambic feet long is a Shakespearean sonnet?

Problem of the Day

70

Bell Work


Number, Number Sense and Operations Standard

7. Find the square root of perfect squares and approximate the square root of nonperfect squares and consecutive integers between which the root lies; e.g., 130 is between 11 and 12.

(pp 18)


Students will learn to find square roots and show understanding through class work.

Learning Objective

(pp 18)


Open yourBooks topage 182.

Open yourBooks topage 182.


Key Terms square root

principal square root

perfect square


Area of a square

s236 square units6


Square Root one of the two equal factors of a number


Every positive number has two square roots, one positive and one negative. One square root of 16 is 4, since 4 • 4 = 16. The other square root of 16 is –4, since (–4) • (–4) is also 16. You can write the square roots of 16 as ±4, meaning “plus or minus” 4.


√16 = 4-√16 = -4

42 = 4 x 4 = 16(-4)2=(-4) x (-4) = 16

±√16 = ±4

You can use the plus or minus symbol, ±, to indicate both square roots.

One square root of 16 is 4, since 4 x 4 =16. The other square root of 16 is 4,since ﴾4﴿﴾4﴿ is also 16. You can writethe square roots of 16 as +4, meaning“plus or minus” 4.


is called the radical sign

Finding the square root of a numberis the inverse of squaring a number.Since 5 = 25 and (5) = 25, the square root of 25 is both 5 and 5.

2 2


Squaring and Square Roots √xx2

5 units

b

1. Find b. Explain your reasoning.

2. Find the area of the square.


Area = 64 un.2a

bWhat if...

1. Find the values of a and b.


** Finding the square root is really finding what number, multiplied by itself twice, will give you the number that is under the radical symbol.


Plug √16 =into your calculator.What do you get?

Principal Square Root = the positive root

REMEMBER the negative root!!!


Find the square roots. (pp 19)


Why wouldn’t the tree fit in the round pot?

It had square roots!

Math Humor


Find the square roots.



Learning Objective

How are we doing???


√ 164

Find the square roots.


Find the square roots. Evaluate.

√4 182


Find the square roots.Evaluate.

3√27 2


7. Estimating Square Roots.



71



71Fill in with

perfect squa

res.64

81



71Fill in with

perfect squa

res.64

81

Find the square rootof each perfectsquare.

8

9


The Question!!!

The is between whattwo integers?

71



71Fill in with

perfect squa

res.

64Find the square rootof each perfectsquare.

8

981

The is between what two integers?71



71Fill in with

perfect squa

res.

64Find the square rootof each perfectsquare.

8

981

The is between what two integers?71

8 and 9


Now we can estimate!!



71

64 8

981

We know the square root is between 8 and 9.

Is it closer to 8 or to 9????

A difference of:



71

64 8

981

We know the square root is between 8 and 9.

Is it closer to 8 or to 9??710

A difference of:

It's a little closer to 8, so I estimate to be about 8.4.

71

8.4


8.

9.


10. Checkpointa. b. c. d.



Learning Objective

How are we doing???


Complete questions 15 in your packet.


1. Describe what is meant by a perfect square. Give an example.

2. Explain how many square roots a positive number can have. How are these square roots different?

3. Decide how many square roots 0 has.


4. The area of a square garden is 1,681 square feet. What are the dimensions of the garden?


5. Tyler's room is a square. The area of his room is 289 square feet. He has a banner that is 18 feet long that he would like to hang on his wall. Will it fit on one wall?



Learning Objective

How are we doing???


p. 184 #1822 all and

p. 188 #2331

Have a great day!

Homework (pp 20)

Problem of the Day Bell Work - Plain Local

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