# Estimating Square Roots by ferda.gurcan

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```									 4-6 Estimating Square Roots
4-6 Estimating Square Roots

Warm Up
Problem of the Day
Lesson Presentation

Course
Course 3 3
4-6 Estimating Square Roots

Warm Up
Find the two square roots of each
number.
1. 144     12        2. 256        16

Evaluate each expression.
3. 8+ 144 20           4. 7   289   119

Course 3
4-6 Estimating Square Roots

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

Course 3
4-6 Estimating Square Roots

Learn to estimate square roots to a given
number of decimal places and solve
problems using square roots.

Course 3
4-6 Estimating Square Roots
Additional Example 1A: Estimating Square Roots of
Numbers
Each square root is between two integers.
Think: What are perfect
55        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.

Course 3
4-6 Estimating Square Roots
Additional Example 1B: Estimating Square Roots of
Numbers Continued
Each square root is between two integers.
Think: What are perfect
– 90
squares close to 90?
–92 = 81   81 < 90

–102 = 100   100 > 90

– 90 is between –9 and –10 because 90 is
between 81 and 100.

Course 3
4-6 Estimating Square Roots
Check It Out: Example 1A

Each square root is between two integers.
Think: What are perfect
80
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.

Course 3
4-6 Estimating Square Roots
Check It Out: Example 1B

Each square root is between two integers.
Name the integers.
Think: What are perfect
– 45
squares close to 45?
–62 = 36     36 < 45

–72 = 49     49 > 45

– 45 is between –6 and –7 because 45 is
between 36 and 49.

Course 3
4-6 Estimating Square Roots
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.

Understand the Problem
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.

Course 3
4-6 Estimating Square Roots

Make a Plan
The length of a side, in feet, is the number
that you multiply by itself to get 500. To be
accurate, find this number to the nearest
tenth. If you do not know a step-by-step
method for finding 500, use guess and
check.

Course 3
4-6 Estimating Square Roots
Solve
Because 500 is between 222 and 232, the square root
of 500 is between 22 and 23.

Guess 22.5             Guess 22.2        Guess 22.4           Guess 22.3
22.52 = 506.25     22.22 = 492.84        22.42 = 501.76       22.32 = 497.29
Too high               Too low           Too high              Too low
Square root is      Square root is       Square root is       Square root is
between 22         between 22.2         between 22.2         between 22.3
and 22.5            and 22.5             and 22.4             and 22.4

2      4       3    1
22.0         22.2        22.4         22.6

The square root is between 22.3 and 22.4.
Course 3
4-6 Estimating Square Roots

Solve

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.

22.352 = 499.5225        Too low
The square root must be greater than 22.35, so
round up.
To the nearest tenth,   500 is about 22.4.
The length of each side of the table is about
22.4 in.
Course 3
4-6 Estimating Square Roots

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.

Course 3
4-6 Estimating Square Roots

Look Back
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,

Course 3
4-6 Estimating Square Roots
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.
Understand the Problem
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.

Course 3
4-6 Estimating Square Roots
Check It Out: Example 2 Continued

Make a Plan
The length of a side, in feet, is the number
that you multiply by itself to get 250. To be
accurate, find this number to the nearest
tenth. If you do not know a step-by-step
method for finding 250, use guess and
check.

Course 3
4-6 Estimating Square Roots
Check It Out: Example 2 Continued
Solve
Because 250 is between 152 and 162, the square
root of 250 is between 15 and 16.
Guess 15.5             Guess 15.9         Guess 15.7           Guess 15.8

15.52 = 240.25       15.92 = 252.81   15.72 = 246.49           15.82 = 249.46

Too Low               Too high            Too Low              Too Low

Square root is       Square root is       Square root is       Square root is
between 15.5         between 15.5         between 15.7         between 15.8
and 16              and 15.9             and 15.9             and 15.9

1            3       4      2
15.5         15.7         15.9         16.1

The square root is between 15.8 and 15.9.
Course 3
4-6 Estimating Square Roots
Check It Out: Example 2 Continued

Solve

To round to the nearest tenth, look at the next
decimal place.
Consider 15.85.      15.852 = 251.2225
The square root is lower than 15.85, so round
down.
To the nearest tenth, 250 is about 15.8.
The length of each side of the garden is

Course 3
4-6 Estimating Square Roots
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.

Course 3
4-6 Estimating Square Roots
Check It Out: Example 2 Continued

Look Back
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,

Course 3
4-6 Estimating Square Roots
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.

Course 3
4-6 Estimating Square Roots
Check It Out: Example 3

Use a calculator to find   800. Round to
the nearest tenth.

Using a calculator,   800 ≈ 28.2842712….

Rounded,   800 is 28.3.

Course 3
4-6 Estimating Square Roots
Lesson Quiz
Each square root is between two integers.
Name the two integers.
1.   27   5 and 6         2. –    456   –22 and –21

Use a calculator to find each value. Round
to the nearest tenth.
3.   89   9.4             4.     1223   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

Course 3

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