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2.7

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Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Find Square Roots and Compare Real Numbers

2.7 Warm-Up

1. 14

ANSWER 196

2. 16

ANSWER 256

Find the square of the number.

<ANSWER

Complete the statements using <, >, or =.

ANSWER <

3. 2.5 – – 198

?

4. 56

2125

?

2.7 Warm-Up

5. A square room has a side length of 25 feet. What isits area?

ANSWER 625 ft2

2.7 Example 1

a. –+ 36 = +– 6 The positive and negative square are 6 and – 6.roots of 36

b. 49 = 7 The positive square root of 49 is 7.

c. 4– = 2– The negative square root of 4 is – 2.

Evaluate the expression.

2.7 Guided Practice

– 1. 9 –= 3

2. 25 = 5


64 3. –+ = 8–+

– 4. 81 = 9–

2.7 Example 2

FURNITURE

The top of a folding table is a square whose area is 945 square inches. Approximate the side length of thetabletop to the nearest inch.

SOLUTION

2 =You need to find the side length s of the tabletop such that s 945. This means that s is the positive square root of 945. You can use a table to determine whether 945 is a perfect square.

2.7 Example 2

As shown in the table, 945 is not a perfect square. The greatest perfect square less than 945 is 900. The least perfect square greater than 945 is 961.

900 < 945 < 961 Write a compound inequality that compares 945 with both 900 and 961.

< < 961900 945 Take positive square root of each number.

30 945< <31 Find square root of each perfect square.

2.7 Example 2

Because 945 is closer to 961 than to 900, is closer to 31 than to 30.

945

ANSWER

The side length of the tabletop is about 31 inches.

2.7 Guided Practice

Approximate the square root to the nearest integer.

5. 32 6

6. 103 10

7. 48– – 7

8. 350– – 19

2.7 Example 3

Tell whether each of the following numbers is a real number, a rational number, an irrational number, an integer, or a whole number: , , – . 24 81 100

NoYes

Real Number?

Whole Number?Integer?

Irrational Number?

Rational Number?

Number

24

100

– 81

Yes No No

Yes Yes No Yes Yes

Yes Yes No Yes No

2.7 Guided Practice

9. Tell whether is a real number, a rational number, an irrational number, an integer, or a whole number.

92

–

ANSWER

real number and rational number

2.7 Example 4

Compare and .4 3

13

SOLUTION

Graph the numbers on a number line.

Because is to the left of , < .

4

3

ANSWER

13 .4

3 13

2.7 Guided Practice

10. Copy and complete using < or >:

(a) – 5 –2.5 ?

14

5(b) ? 7

ANSWER

>

ANSWER

<

2.7 Example 5

Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample.

SOLUTION

a. Given: No fractions are irrational numbers.

If-then form: If a number is a fraction, then it is not an irrational number.

The statement is true.

2.7 Example 5

b.

Given: All real numbers are rational numbers.

The statement is false. For example, is a real number but not a rational number.

2

If-then form: If a number is a real number, then it is a rational number.

2.7 Guided Practice


All square roots of perfect squares are rational numbers.

11.

If-then form: If a number is the square root of perfect square, then it is a rational number.


2.7 Guided Practice


All repeating decimals are irrational numbers. 12.

If-then form: If a number is a repeating decimal, then it is an irrational number.

The statement is false. For example, 0.333… is a repeating decimal and can be written as , so it is a rational number.

13

2.7 Guided Practice


No integers are irrational numbers. 13.

If-then form: If a number is an integer, then it is not an irrational number.


2.7 Lesson Quiz


Approximate the square root to the nearest integer.

1.

–+ 289

ANSWER –+17

2. 36–

3. 21–

ANSWER – 5

ANSWER – 6

4. 620

ANSWER 25

2.7 Lesson Quiz

A square courtyard has an area of 272 square feet. What is the side length of the courtyard to the nearest foot?

5.

ANSWER 16 ft

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