1. Math fact:
The sum of any number of consecutive odd whole numbers, beginning with 1, is a perfect square
e.g. 1+3=4, 1+3+5=9, =16

2. Example 1: Estimating Square Roots of Numbers
The 55 is between two integers. Name the integers. Explain your answer. 55
36, 49, 64, 81
List perfect squares near 55.
49 < 55 < 64
Find the perfect squares nearest 55.
49 < 55 < 64
Find the square roots of the perfect squares.
7 < 55 < 8
55 is between 7 and 8 because 55 is between 49 and 64.

3. Example 2: Approximating Square Roots to the Nearest Hundredth
Approximate √135 to the nearest hundredth.
Step 1 Find the value of the whole number.
121 < 135 < 144
Find the perfect squares nearest 135.
√121 <
√135 <
144 √
Find the square roots of the perfect squares.
11 <
135
< 12 √
The number will be between 11 and 12.
The whole number part of the answer is 11.

4. Example 2 Continued
Approximate √135 to the nearest hundredth.
Step 2 Find the value of the decimal.
Find the difference between the given number, 135, and the lower perfect square.
135 – 121 = 14
Find the difference between the greater perfect square and the lower perfect square.
144 – 121 = 23
1423
Write the difference as a ratio.
Divide to find the approximate decimal value.
14 ÷ 23 ≈ 0.609

5. Approximate √135 to the nearest hundredth.
Example 2 Continued
Approximate √135 to the nearest hundredth.
Step 3 Find the approximate value.
Combine the whole number and decimal. =
≈ 11.61
Round to the nearest hundredth.
The approximate value of to the nearest hundredth is

6. Example 3: Using a Calculator to Estimate the Value of a Square Root
Use a calculator to find Round to the nearest tenth.
600 ≈ …
Use a calculator.
600 ≈ 24.5
Round to the nearest tenth.
600 rounded to the nearest tenth is 24.5.