1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Find the two square roots of each number.
Warm Up
Find the two square roots of each number.
Evaluate each expression.
12
16 20
119

3. 3-6
Learn to estimate square roots and solve problems using square roots. 3

4. Example 1: Estimating Square Roots of Numbers
A. The square root is between two integers. Name the integers. Explain your answer.
Think: What are perfect squares close to 55? 55
72 = 49
49 < 55
82 = 64
64 > 55
55 is between 7 and 8 because 55 is between 49 and 64. 4

5. Example 1: Estimating Square Roots of Numbers Continued
B. The square root is between two integers. Name the integers. Explain your answer.
Think: What are perfect squares close to 90? – 90
–92 = 81
81 < 90
–102 = 100
100 > 90
is between –9 and –10 because 90 is between 81 and 100. 90 – 5

6. Think: What are perfect squares close to 80? 80
Check It Out
C. The square root is between two integers. Name the integers. Explain your answer.
Think: What are perfect squares close to 80? 80
82 = 64
64 < 80
92 = 81
81 > 80
80 is between 8 and 9 because 80 is between 64 and 81. 6

7. D. The square root is between two integers. Name the integers.
Check It Out
D. The square root is between two integers. Name the integers.
Think: What are perfect squares close to 45? – 45
(–6)2 = 36
36 < 45
(–7)2 = 49
49 > 45
is between –6 and –7 because 45 is between 36 and 49. 45 – 7

8. Example 2: Application
A. You want to sew a fringe on a square tablecloth with an area of 500 square inches. Calculate the length of each side of the tablecloth and the length of fringe you will need to the nearest tenth of an inch.
The length of each side of the square is
√500 .
484 < 500 < 529
List the perfect squares nearest 500.
Find the square roots of the perfect squares.
The number will be between 22 and 23.
The length of each side of the table is about 22.4 in., and you will need about 89.6 in. of fringe.

9. Example 3: Approximating Square Roots to the Nearest Hundredth
A. Approximate to the nearest hundredth.
Step 1: Find the value of the whole number.
121 < 141 < 144
Find the perfect squares nearest 141.
Find the square roots of the perfect
squares.
The number will be between 11 and
12.
The whole number part of the answer is 11.

10. Additional Example 3 Continued
Approximate to the nearest hundredth.
Step 2: Find the value of the decimal.
Find the difference between the given
number, 141, and the lower perfect
square.
141 – 121 = 20
Find the difference between the
greater perfect square and the lower
perfect square.
144 – 121 = 23 20 23
Write the difference as a ratio.
Divide to find the approximate
decimal value.
20  3 ≈ 0.869

11. Additional Example 3 Continued
Approximate to the nearest hundredth.
Step 3: Find the approximate value.
Combine the whole number and
decimal. =
≈ 11.87
Round to the nearest hundredth.
The approximate value of to the nearest
hundredth is

12. Example 4: Using a Calculator to Estimate the Value of a Square Root
A. Use a calculator to find Round to the nearest tenth.
Using a calculator, ≈ ….
Rounded, is 24.5. 12

13. Use a calculator to find 800. Round to the nearest tenth.
Check It Out: Example 4
Use a calculator to find Round to the nearest tenth.
Using a calculator, ≈ ….
Rounded, is 28.3. 13

14. Lesson Quiz 14

15. Each square root is between two integers. Name the two integers.
Lesson Quiz
Each square root is between two integers. Name the two integers.
– 456
5 and 6
–22 and –21
Use a calculator to find each value. Round to the nearest tenth.
9.4
35.0
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?
179 ft 15