learn to estimate square roots and solve problems using square roots

Learn to estimate square roots and solve problems using square roots.

Example 1: Estimating Square Roots of Numbers

The square root is between two integers. Name the integers. Explain your answer.

55Think: What are perfect squares close to 55?

72 = 49 49 < 55

82 = 64 64 > 55

55 is between 7 and 8 because 55 is between 49 and 64.

90–

Example 2: Estimating Square Roots of Numbers Continued

Think: What are perfect squares close to 90?

–92 = 81 81 < 90

–102 = 100 100 > 90

The square root is between two integers. Name the integers. Explain your answer.

is between –9 and –10 because 90 is between 81 and 100.

90–

Example 3

The square root is between two integers. Name the integers. Explain your answer.

80Think: What are perfect squares close to 80?

82 = 64 64 < 80

92 = 81 81 > 80

80 is between 8 and 9 because 80 is between 64 and 81.

45–

The square root is between two integers. Name the integers.

Think: What are perfect squares close to 45?

–62 = 36 36 < 45

–72 = 49 49 > 45

Example 4

is between –6 and –7 because 45 is between 36 and 49.

45–

11.869

Round to the nearest hundredth.11.869 ≈ 11.87

Approximate to the nearest hundredth.

Example 5

The approximate value of to the nearesthundredth is 11.87.

15.484

Round to the nearest hundredth.15.484 ≈ 15.48

Example 6

Approximate to the nearest hundredth.

The approximate value of to the nearesthundredth is 15.48.

Example 7: Using a Calculator to Estimate the Value of a Square Root

Using a calculator, 600 ≈ 24.49489742….

Rounded, 600 is 24.5.

Use a calculator to find 600. Round to the nearest tenth.

Example 8

Rounded, 800 is 28.3.

Using a calculator, 800 ≈ 28.2842712….

Use a calculator to find 800. Round to the nearest tenth.

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Lesson Quiz

Each square root is between two integers. Name the two integers.

1. 27 2. – 456

Use a calculator to find each value. Round to the nearest tenth.

3. 89 4. 1223

5. A square field has an area of 2000 square feet. To the nearest foot, how much fencing would be needed to enclose the field?

5 and 6 –22 and –21

9.4 35.0

179 ft

1. Name the two integers the square root is between.

A. 5 and 6

B. 6 and 7

C. 8 and 9

D. 38 and 40

Lesson Quiz for Student Response Systems

2. Use a calculator to round to the nearest tenth.

A. 2.3

B. 4.5

C. 6.7

D. 9.2

Lesson Quiz for Student Response Systems

3. Name the two integers the square root is between.

A. –2 and –3

B. –10 and –11

C. –15 and –14

D. –15 and –16

Lesson Quiz for Student Response Systems