Course 3

4-6 Estimating Square Roots

Warm UpFind the two square roots of each number.

Evaluate each expression.

12 16

20 119

1. 144 2. 256

3. 8+ 144 4. 7 2895. A square window has an area of 169 square inches, how wide is the window?

6. 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?

Course 3

4-6 Estimating Square Roots

Learn to estimate square roots to a given number of decimal places and solve problems using square roots.

Course 3

4-6

Course 3

4-6 Estimating Square Roots

Estimating Square Roots of Numbers

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

Explain your answer.

Course 3

4-6 Estimating Square Roots

Example 1

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.

Course 3

4-6 Estimating Square Roots

90–

Example 2

Think: What are perfect squares close to 90?

–92 = 81 81 < 90

–102 = 100 100 > 90

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

90–

Course 3

4-6 Estimating Square Roots

Example 3

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.

Course 3

4-6 Estimating Square Roots

45– 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–

Course 3

4-6 Estimating Square Roots

Estimating Large Square Roots

Use a calculator to find answer, round to the nearest tenth.

Course 3

4-6 Estimating Square Roots

Example 5

Using a calculator, 600 ≈ 24.49489742….

Rounded, 600 is 24.5.

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

Course 3

4-6 Estimating Square Roots

Example 6

Rounded, 800 is 28.3.

Using a calculator, 800 ≈ 28.2842712….

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

Course 3

4-6 Estimating Square Roots

Lesson Summary

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