Page 142 & Spiral Review Answers

Pre-Algebra

3-8 Squares and Square Roots

Student Learning Goal Chart

Lesson Reflections

3-8

Pre-Algebra Learning Goal

Students will understand rational and real numbers.

Students will understand rational and real numbers by being able to do the following:

• Learn to write rational numbers in equivalent forms (3.1)

• Learn to add and subtract decimals and rational numbers with like denominators (3.2)

• Learn to add and subtract fractions with unlike denominators (3.5)

• Learn to multiply fractions, decimals, and mixed numbers (3.3)

• Learn to divide fractions and decimals (3.4)

• Learn to solve equations with rational numbers (3.6)

• Learn to solve inequalities with rational numbers (3-7)

• Learn to find square roots (3-8)

Pre-Algebra

3-8 Squares and Square Roots

Today’s Learning Goal Assignment

Learn to find square roots.

Squares and Square Roots

Pre-Algebra

3-8 Squares and Square Roots

Pre-Algebra HW

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Pre-Algebra

3-8 Squares and Square Roots3-8 Squares and Square Roots

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

3-8 Squares and Square Roots

Warm UpSimplify.

Pre-Algebra

3-8 Squares and Square Roots

25 64

144 225

400

1. 52 2. 82

3. 122 4. 152

5. 202

Pre-Algebra

3-8 Squares and Square Roots

Problem of the DayA 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?

70

Pre-Algebra

3-8 Squares and Square Roots

Today’s Learning Goal Assignment

Learn to find square roots.

Squares and Square Roots

Pre-Algebra

3-8 Squares and Square Roots

Vocabularyprincipal square rootperfect square

Pre-Algebra

3-8 Squares and Square Roots

Think about the relationship between the area of a square and the length of one of its sides.

Taking the square root of a number is the inverse of squaring the 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 root of 16 as ±4, meaning “plus or minus” 4.

area = 36 square unitsside length = 36 = 6 units

62 = 36 36 = 6

Pre-Algebra

3-8 Squares and Square Roots

The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number that has integers as its square roots. Other perfect squares include 1, 4, 9, 25, 64, and 81.

When you press the key on a calculator, only the nonnegative square root appears. This is called the principal square root of the number.

+ 16 = 4 – 16 = –4

–49 is not the same as – 49. A negative number has no real square root.

Helpful Hint

Pre-Algebra

3-8 Squares and Square Roots

Additional Example: 1 Finding the Positive and Negative Square Roots of a Number

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.

Pre-Algebra

3-8 Squares and Square Roots

A. 25

Try This: 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. 289289 = 17

289 = –17–

17 is a square root, since 17 • 17 = 289.

–17 is also a square root, since –17 • –17 = 289.

Pre-Algebra

3-8 Squares and Square Roots

132 = 169

The window is 13 inches wide.

Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning.

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

So 169 = 13.

Pre-Algebra

3-8 Squares and Square Roots

The table will fit through the door.

Find the square root of 16 to find the width of the table. Use the positive square root; a negative length has no meaning.

Try This: 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?

So the table is 4 feet wide, which is less than 5 feet.

16 = 4

Pre-Algebra

3-8 Squares and Square Roots

Additional Example 3: Evaluating Expressions Involving Square Roots

Evaluate the expression.

A. 3 36 + 7

Evaluate the square root.

Add.= 25

B. 21 – 5 + 9 Evaluate the expression under the square root symbol.

Evaluate the square root.

Multiply.= 18 + 7

= 4 + 9

= 13 Add.

3 36 + 7 = 3(6) + 7

21 – 5 + 9 = 16 + 9

Pre-Algebra

3-8 Squares and Square Roots

Try This: Example 3

Evaluate the expression.

A. 2 25 + 4

Evaluate the square root.

Add.= 10

B. 41 – 5 + 5Evaluate the expression under the square root symbol.Evaluate the square root.

Multiply.= 10 + 4

= 6 + 5= 11

Add.

2 25 + 4 = 2(5) + 4

41 – 5 + 5 = 36 + 5

Pre-Algebra

3-8 Squares and Square Roots

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 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