 # Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Warm Up Warm.

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Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Warm Up Simplify. 8. Write the rule in words and as an equation. 25 64 144225 400 1. 5 2 2. 8 2 3. 12 2 4. 15 2 5. 20 2. 6. Evaluate (–3) 4 81 7. Evaluate g h + 3 k – g k for g = 2, h = 4, and k = 3. 7 X5101520 Y10203040

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 CMT Question of the day! And Check Homework…

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 4-4 Lesson Quiz Write each number in standard notation. 1. 1.72  10 4 2. 6.9  10 –3 4. 57,000,000 17,200 0.0069 3. 0.0053 5.3  10 –3 5.7  10 7 Write each number in scientific notation. 5. Write the rule in words and as an equation. T Divide by 2, Y = x/2 X246810 Y12345

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Learn to find square roots. 4-5

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 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.

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 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 = ______________

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 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?

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Try This Write 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.

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 6 2 = 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.

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 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. 10 is a square root, since 10 10 = 100. –10 is also a square root, since –10 –10 = 100. 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.

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 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. 12 is a square root, since 12 12 = 144. –12 is also a square root, since –12 –12 = 144. 25 = –5 – 25 = 5 144 = 12 144 = –12 – Find the two square roots of each number. B. 144 C. 289 289 = 17 289 = –17 – 17 is a square root, since 17 17 = 289. –17 is also a square root, since –17 –17 = 289.

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 13 2 = 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: Application A square window has an area of 169 square inches. How wide is the window? So 169 = 13. The area of a square is s 2, where s is the length of a side. Remember!

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Write and solve an equation to find the area of the kitchen table Check It Out: Example 2 A 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

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Additional Example 3A: Evaluating Expressions Involving Square Roots Simplify the expression. Evaluate the square root. Add. = 25 Multiply. = 18 + 7 3 36 + 7 3 36 + 7 = 3(6) + 7

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Additional Example 3B: Evaluating Expressions Involving Square Roots Simplify the expression. + 25 16 3434 3434 + 3434 = + 1.5625 Evaluate the square roots. = 1.25 + 3434 25 16 = 1.5625. = 2 Add.

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Check It Out: Example 3A Simplify the expression. Evaluate the square root. Add.= 14 Multiply.= 10 + 4 2 25 + 4 2 25 + 4 = 2(5) + 4

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Check It Out: Example 3B Simplify the expression. + 18 t2 1414 1414 + 1414 = + 9 Evaluate the square roots. = 3 + 1414 18 t2 = 9. = 3 Add. 1414

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 Lesson Quiz Find the two square roots of each number. 1. 81 2. 2500 Evaluate each expression. 3. 3 16 + 1 4. 7 9 – 2 49 9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 ft 2. How much fencing does she need? 45 ft

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 1. Find two square roots of each number. 64 A. 4 B. 8 C. 9 D. 16 Lesson Quiz for Student Response Systems

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 2. Find two square roots of each number. 6400 A. 4 B. 8 C. 80 D. 800 Lesson Quiz for Student Response Systems

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 3. Evaluate the expression. A. 17 B. 17 C. 19 D. 72 Lesson Quiz for Student Response Systems

Squares and Square Roots Students will be able to find square roots. Students will describe in writing what is meant by a perfect square. 4-5 4. Evaluate the expression. A. 4 B. 8 C. 16 D. 40 Lesson Quiz for Student Response Systems

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