squares and square roots students will be able to find square roots. students will describe in...

Squares and Square RootsStudents will be able to find square roots.Students will describe in writing what is meant by a perfect square.

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


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Warm UpSimplify.

8. Write the rule in words and as an equation.

25 64

144 225400

1. 52 2. 82

3. 122 4. 152

5. 202.

6. Evaluate (–3)4 81

7. Evaluate gh + 3k – gk for g = 2, h = 4, and k = 3.

7X 5 10 15 20

Y 10 20 30 40


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CMT Question of the day!

And Check Homework…


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4-4 Lesson Quiz

Write each number in standard notation.

1. 1.72 104

2. 6.9 10–3

4. 57,000,000

17,200

0.0069

3. 0.0053 5.3 10–3

5.7 107

Write each number in scientific notation.

5. Write the rule in words and as an equation. T

Divide by 2, Y = x/2

X 2 4 6 8 10

Y 1 2 3 4 5


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Learn to find square roots.

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Shade in graph paper to make each of the shapes below. Each shape is a

square.

Count and write the number of square tiles in each of the larger squares below.1. 2. 3.


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Count and write the number of square tiles in each of the larger squares below.1. 2. 3.

Continue to draw larger squares. Make one that is 7 tiles wide and 7 tiles high; then make one that is 8 wide and 8 high. Count the number of squares in each shape.

4. 7 by 7 = ___________ 5. 8 by 8 = ______________


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Continue to draw larger squares. Make one that is 7 tiles wide and 7 tiles high; then make one that is 8 wide and 8 high. Count the number of squares in each shape.

4. 7 by 7 = ____ 5. 8 by 8 = _______

Talk in your groups about the following questions. Be prepared to discuss them if I call on you.The numbers 1, 4, 9, 16, 25, etc. are known as perfect squares. Why do you think they are called perfect squares?

How are the width and the height of the squares related? How are they related to the total number of tiles?

How could you find the next numbers that are perfect squares without tiles?


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Try ThisWrite down the first 10 perfect squares, starting with 0.0, 1, 4, 9, ___, ___, ___, ___, ___, ___

Now subtract each number from the one after it. 1 , 3 , 5 , ___, ___, ___, ___, ___

What pattern do you see in the difference between two perfect squares?

Use your answer from Exercise 3 above to find all perfect squares less than 200.


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62 = 36 36 = 6

-What’s the opposite operation to addition?

-What’s the opposite operation to multiplication?

-The opposite operation to squaring a number is taking the square root.


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Find the two square roots of each number.

7 is a square root, since 7 • 7 = 49.

–7 is also a square root, since –7 • –7 = 49.



49 = –7–

49 = 7

100 = 10

100 = –10–

A. 49

B. 100

C. 225

15 is a square root, since 15 • 15 = 225.225 = 15

225 = –15– –15 is also a square root, since –15 • –15 = 225.


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A. 25

Check It Out: Example 1

5 is a square root, since 5 • 5 = 25.–5 is also a square root, since –5 • –5 = 25.



25 = –5–25 = 5

144 = 12

144 = –12–


B. 144

C. 289289 = 17

289 = –17–




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132 = 169

Use the positive square root; a negative length has

no meaning. The window is 13 inches wide.

Write and solve an equation to find the area of the window.

Additional Example 2: ApplicationA square window has an area of 169 square inches. How wide is the window?

So 169 = 13.

The area of a square is s2, where s is the length of a side.

Remember!


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Write and solve an equation to find the area of the kitchen table

Check It Out: Example 2A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?

Use the positive square root; a negative length has no meaning. So the table is 4 feet wide, which is less than 5 feet, so it will fit through the van door.

16 = 4


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Additional Example 3A: Evaluating Expressions Involving Square RootsSimplify the expression.

Evaluate the square root.

Add.= 25

Multiply.= 18 + 7

3 36 + 7

3 36 + 7 = 3(6) + 7


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Additional Example 3B: Evaluating Expressions Involving Square RootsSimplify the expression.

+ 25 16

3 4

25 16

3 4

+3 4 = +1.5625

Evaluate the square roots.

= 1.25 + 3 4

25 16

= 1.5625.

= 2 Add.


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Check It Out: Example 3ASimplify the expression.

Evaluate the square root.

Add.= 14

Multiply.= 10 + 4

2 25 + 4

2 25 + 4 = 2(5) + 4


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Check It Out: Example 3BSimplify the expression.

+ 18 t2

1 4

18 t2

1 4

+ 1 4

= + 9

Evaluate the square roots.= 3 + 1 4

18 t2

= 9.

= 3 Add.1 4


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Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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Lesson Quiz


1. 81 2. 2500

Evaluate each expression.

3. 3 16 + 1 4. 7 9 – 2 49

9 50

13 7

5. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft2. How much fencing does she need?45 ft


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1. Find two square roots of each number.

64

A. 4

B. 8

C. 9

D. 16



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2. Find two square roots of each number.

6400

A. 4

B. 8

C. 80

D. 800



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3. Evaluate the expression.

A. 17

B. 17

C. 19

D. 72



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4. Evaluate the expression.

A. 4

B. 8

C. 16

D. 40
