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Estimating Square Roots
Warm Up
Lesson PresentationProblem of the Day
Lesson Quizzes
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. 7 289
Estimating Square Roots
Problem of the DayA pyramid of blocks is built in layers. The bottom layer has 62, or 36, blocks. The next layer has 52 blocks, and so on until the top layer has 1 block. How many blocks are there in all?91 blocks
Estimating Square Roots
Learn to estimate square roots and solve problems using square roots.
Estimating Square Roots
Additional Example 1A: 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.
Estimating Square Roots
90–
Additional Example 1B: 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–
Estimating Square Roots
Check It Out: Example 1A
The square root is between two integers. Name the integers. Explain your answer.
80 Think: 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.
Estimating Square Roots
45–
The square root is between two integers. Name the integers.
Think: What are perfect squares close to 45?
(–6)2 = 36 36 < 45
(–7)2 = 49 49 > 45
Check It Out: Example 1B
is between –6 and –7 because 45 is between 36 and 49.
45–
Estimating Square Roots
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.
Additional Example 2: Application
484 < 500 < 529 List the perfect squares nearest 500.
Find the square roots of the perfect squares.
The length of each side of the table is about 22.4 in., and you will need about 89.6 in. of fringe.
The number will be between 22 and 23.
The length of each side of the square is √500 .
Estimating Square RootsCheck 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 List the perfect squares nearest 168.
Find the square roots of 144 and 169.
< < √168√144 √169
12 < < 13√168
√168 ≈ 13
Each side of the tent is about 13 feet long.
168 is closer to 169 than to 144.
Estimating Square Roots
Approximate to the nearest hundredth.
Additional Example 3: Approximating Square Roots to the Nearest Hundredth
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.
Step 1: Find the value of the whole number.
Estimating Square Roots
Approximate to the nearest hundredth.
Additional Example 3 Continued
141 – 121 = 20Find the difference between the givennumber, 141, and the lower perfect square.Find the difference between the greater perfect square and the lowerperfect square.
Write the difference as a ratio.
20 ÷ 3 ≈ 0.869
Step 2: Find the value of the decimal.
144 – 121 = 23
2023
Divide to find the approximate decimal value.
Estimating Square Roots
11 + 0.869 = 11.869 Combine the whole number anddecimal.
Round to the nearest hundredth.
Step 3: Find the approximate value.
11.869 ≈ 11.87
Approximate to the nearest hundredth.
Additional Example 3 Continued
The approximate value of to the nearesthundredth is 11.87.
Estimating Square Roots
Approximate to the nearest hundredth.
Check It Out: Example 3
225 < 240 < 256 Find the perfect squares nearest 240.
Find the square roots of the perfect squares.
The number will be between 15 and 16.
The whole number part of the answer is 15.
Step 1: Find the value of the whole number.
Estimating Square Roots
Check It Out: Example 3 Continued
240 – 225 = 15Find the difference between the givennumber, 240, and the lower perfect square.Find the difference between the greater perfect square and the lowerperfect square.
Write the difference as a ratio.
15 ÷ 31 ≈ 0.484
Step 2: Find the value of the decimal.
256 – 225 = 31
1531
Divide to find the approximate decimal value.
Approximate to the nearest hundredth.
Estimating Square Roots
15 + 0.484 = 15.484 Combine the whole number anddecimal.
Round to the nearest hundredth.
Step 3: Find the approximate value.
15.484 ≈ 15.48
Check It Out: Example 3 Continued
Approximate to the nearest hundredth.
The approximate value of to the nearesthundredth is 15.48.
Estimating Square Roots
Additional Example 4: 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.
Estimating Square Roots
Check It Out: Example 4
Rounded, 800 is 28.3.
Using a calculator, 800 ≈ 28.2842712….
Use a calculator to find 800. Round to the nearest tenth.
Estimating Square Roots
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
Estimating Square Roots
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
Estimating Square Roots
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
Estimating Square Roots
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
Estimating Square Roots
3. Name the two integers the square root is between.
A. –2 and –3
B. –10 and –11
C. –13 and –14
D. –15 and –16
Lesson Quiz for Student Response Systems
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