1. 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

2. Example 1: Estimating Square Roots of Numbers
The square root is between two integers. Name the integers. Explain your answer.
Think: What are perfect squares close to 55?
Think: What are perfect squares close to 90? A. 55 – B. 90
(–9)2 = 81
72 = 49
81 < 90
49 < 55
82 = 64
64 > 55
(–10)2 = 100
100 > 90 2

3. Example 1: Estimating Square Roots of Numbers
The square root is between two integers. Name the integers. Explain your answer. C. D.
Think: What are perfect squares close to 80? –
Think: What are perfect squares close to 45? 80 45
82 = 64
64 < 80
(–6)2 = 36
36 < 45
92 = 81
81 > 80
(–7)2 = 49
49 > 45 3

4. Example 2: Application
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
The length of each side of the table is about 22.4 in., and you will need about 89.6 in. of fringe.

5. Check It Out: Example 2
A tent was advertised in the newspaper as having an enclosed square area of 168 ft2. What is the approximate length of the sides of the square area? Round your answer to the nearest foot.
The length of each side of the square is
√168
144 < 168 < 169
<
√168
√144
√169
12 < < 13
√168
√168  13 feet

6. Example 3: Approximating Square Roots to the Nearest Hundredth
Approximate to the nearest hundredth.
Step 1: Find the value of the whole number.
121 < 141 < 144
whole number part  11
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.
≈ 0.869
Divide to find the approximate decimal value.
Step 3: Find the approximate value. =
≈ 11.87

7. Example 4: Using a Calculator to Estimate the Value of a Square Root
Use a calculator to find Round to the nearest tenth.
Using a calculator, ≈ ….
Rounded, is 24.5. 7

8. 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 8