Estimating Square Roots

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4-6
Estimating Square Roots
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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Warm Up Find the two square roots of each
number. Evaluate each expression.
1. 144 2. 256
12
16
20
119
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Problem of the Day A 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
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4-6
Learn to estimate square roots to a given number
of decimal places and solve problems using square
roots.
Course 3
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Additional Example 1A Estimating Square Roots of
Numbers
Each square root is between two integers. Name
the integers. Explain your answer.
Think What are perfect squares close to 55?
55
49 lt 55
72 49
64 gt 55
82 64
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Additional Example 1B Estimating Square Roots of
Numbers Continued
Each square root is between two integers. Name
the integers. Explain your answer.
Think What are perfect squares close to 90?
90

81 lt 90
92 81
100 gt 90
102 100
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Check It Out Example 1A
Each square root is between two integers. Name
the integers. Explain your answer.
Think What are perfect squares close to 80?
80
64 lt 80
82 64
81 gt 80
92 81
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Check It Out Example 1B
Each square root is between two integers. Name
the integers.
Think What are perfect squares close to 45?
45

36 lt 45
62 36
49 gt 45
72 49
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Additional Example 2 Problem Solving 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.
First find the length of a side. Then you can use
the length of a side to find the perimeter, the
length of fringe around the tablecloth.
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Additional Example 2 Continued
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Additional Example 2 Continued
Because 500 is between 222 and 232, the square
root of 500 is between 22 and 23.
The square root is between 22.3 and 22.4.
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Additional Example 2 Continued
The square root is between 22.3 and 22.4. To
round to the nearest tenth, look at the next
decimal place.
Consider 22.35.
Too low
22.352 499.5225
The square root must be greater than 22.35, so
round up.
The length of each side of the table is about
22.4 in.
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Additional Example 2 Continued
Solve
The length of a side of the tablecloth is 22.4
inches, to the nearest tenth of an inch. Now
estimate the length around the tablecloth.
4 22.4 89.6
Perimeter 4 side
You will need about 89.6 inches of fringe.
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Additional Example 2 Continued
The length 90 inches divided by 4 is 22.5 inches.
A 22.5-inch square has an area of 506.25 square
inches, which is close to 500, so the answers are
reasonable.
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Check It Out Example 2
You want to build a fence around a square garden
that is 250 square feet. Calculate the length of
one side of the garden and the total length of
the fence, to the nearest tenth.
First find the length of a side. Then you can use
the length of a side to find the perimeter, the
length of the fence.
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Check It Out Example 2 Continued
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Check It Out Example 2 Continued
Because 250 is between 152 and 162, the square
root of 250 is between 15 and 16.
Guess 15.5
15.52 240.25
Too Low
Square root is between 15.5 and 16
Guess 15.9
15.92 252.81
Too high
Square root is between 15.5 and 15.9
Guess 15.7
15.72 246.49
Too Low
Square root is between 15.7 and 15.9
Guess 15.8
15.82 249.46
Too Low
Square root is between 15.8 and 15.9
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2
3
4
The square root is between 15.8 and 15.9.
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Check It Out Example 2 Continued
To round to the nearest tenth, look at the next
decimal place.
15.852 251.2225
Consider 15.85.
The square root is lower than 15.85, so round
down.
The length of each side of the garden is about
15.8 ft.
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Check It Out Example 2 Continued
Solve
The length of a side of the garden is 15.8 feet,
to the nearest tenth of a foot. Now estimate the
length around the garden.
4 15.8 63.2
Perimeter 4 side
You will need about 63.2 feet of fence.
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Check It Out Example 2 Continued
The length 63.2 feet divided by 4 is 15.8 feet. A
15.8 foot square has an area of 249.64 square
feet, which is close to 250, so the answers are
reasonable.
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Additional Example 3 Using a Calculator to
Estimate the Value of a Square Root
Use a calculator to find 600. Round to the
nearest tenth.
Using a calculator, 600 24.49489742.
Rounded, 600 is 24.5.
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Check It Out Example 3
Use a calculator to find 800. Round to the
nearest tenth.
Rounded, 800 is 28.3.
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Lesson Quiz
Each square root is between two integers. Name
the two integers.
1. 27 2. 456
5 and 6
22 and 21
Use a calculator to find each value. Round to the
nearest tenth.
9.4
35.0
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?
179 ft