Transcript 3-9

Square
Roots
3-9
3-9 Finding
Finding
Square
Roots
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
3-9 Finding 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
Pre-Algebra
4. 7
289
119
3-9 Finding 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
Pre-Algebra
3-9 Finding Square Roots
Learn to estimate square roots to a given
number of decimal places and solve
problems using square roots.
Pre-Algebra
3-9 Finding Square Roots
A museum director wants to install a
skylight to illuminate an unusual piece of
art. It must be square and have an area of
300 square inches, with wood trim around
it. Can you calculate the trim that you
need? You can do this by using your
knowledge of squares and square roots.
Pre-Algebra
3-9 Finding Square Roots
Additional Example 1A: Estimating Square Roots of
Numbers
Each square root is between two integers.
Name the integers.
55
A.
Think: What are perfect
squares close to 55?
72 = 49
49 < 55
82 = 64
64 > 55
55 is between 7 and 8.
Pre-Algebra
7<
55 < 8
3-9 Finding Square Roots
Additional Example 1B: Estimating Square Roots of
Numbers Continued
Each square root is between two integers.
Name the integers.
Think: What are perfect
B. – 90
squares close to 90?
–92 = 81
81 < 90
–102 = 100
100 > 90
– 90 is between –9 and –10. –9 < –
Pre-Algebra
90 < –10
3-9 Finding Square Roots
Try This: Example 1A
Each square root is between two integers.
Name the integers.
A.
80
Think: What are perfect
squares close to 80?
82 = 64
64 < 80
92 = 81
81 > 80
80 is between 8 and 9.
Pre-Algebra
8<
80 < 9
3-9 Finding Square Roots
Try This: Example 1B
Each square root is between two integers.
Name the integers.
B. – 45
Think: What are perfect
squares close to 45?
–62 = 36
36 < 45
–72 = 49
49 > 45
– 45 is between –6 and –7.
Pre-Algebra
–6 < – 45 < –7
3-9 Finding 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.
Pre-Algebra
3-9 Finding Square Roots
Additional Example 2 Continued
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.
Pre-Algebra
3-9 Finding Square Roots
Additional Example 2 Continued
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
between 22
and 22.5
Square root is
between 22.2
and 22.5
Square root is
between 22.2
and 22.4
Square root is
between 22.3
and 22.4
2
22.0
22.2
4
3
22.4
1
22.6
The square root is between 22.3 and 22.4.
Pre-Algebra
3-9 Finding Square Roots
Additional Example 2 Continued
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.
Pre-Algebra
3-9 Finding Square Roots
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.
Pre-Algebra
3-9 Finding Square Roots
Additional Example 2 Continued
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,
so the answers are reasonable.
Pre-Algebra
3-9 Finding Square Roots
Try This: 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.
Pre-Algebra
3-9 Finding Square Roots
Try This: 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.
Pre-Algebra
3-9 Finding Square Roots
Try This: 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
between 15.5
and 16
Square root is
between 15.5
and 15.9
Square root is
between 15.7
and 15.9
Square root is
between 15.8
and 15.9
1
15.5
3
15.7
4
2
15.9
16.1
The square root is between 15.8 and 15.9.
Pre-Algebra
3-9 Finding Square Roots
Try This: 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
about 15.8 ft.
Pre-Algebra
3-9 Finding Square Roots
Try This: 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.
Pre-Algebra
3-9 Finding Square Roots
Try This: 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,
so the answers are reasonable.
Pre-Algebra
3-9 Finding Square Roots
Additional Examples 3: Using a Calculator to
Estimate the Value of a Square Root
Use a calculator to find
the nearest tenth.
Using a calculator,
Rounded,
Pre-Algebra
500. Round to
500 ≈ 22.36067977….
500 is 22.4.
3-9 Finding Square Roots
Try This: Example 3
Use a calculator to find
the nearest tenth.
Using a calculator,
Rounded,
Pre-Algebra
200. Round to
200 ≈ 14.14213562….
200 is 14.1.
3-9 Finding 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
Pre-Algebra