Transcript Estimating Square Roots

3-6 Estimating Square Roots
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
3-6 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
3-6 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
3-6 Estimating Square Roots
Learn to estimate square roots and solve
problems using square roots.
3-6 Estimating Square Roots
Additional Example 1A: Estimating Square Roots of
Numbers
The square root is between two integers.
Name the integers. Explain your answer.
55
Think: 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.
3-6 Estimating Square Roots
Additional Example 1B: Estimating Square Roots of
Numbers Continued
The square root is between two integers.
Name the integers. Explain your answer.
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.
3-6 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.
3-6 Estimating Square Roots
Check It Out: Example 1B
The square root is between two integers.
Name the integers.
– 45
Think: What are perfect
squares close to 45?
(–6)2 = 36
36 < 45
(–7)2 = 49
49 > 45
– 45 is between –6 and –7 because 45 is
between 36 and 49.
3-6 Estimating Square Roots
Additional Example 2: 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.
The length of each side of the square is √500 .
484 < 500 < 529
List the perfect squares nearest 500.
Find the square roots of the perfect
squares.
The number will be between
22 and 23.
The length of each side of the table is about 22.4 in., and
you will need about 89.6 in. of fringe.
3-6 Estimating Square Roots
Check 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.
√144 < √168 <√169
12 < √16 < 13
8
√168  13
Find the square roots of 144 and 169.
168 is closer to 169 than to 144.
Each side of the tent is about 13 feet long.
3-6 Estimating Square Roots
Additional Example 3: Approximating Square Roots
to the Nearest Hundredth
Approximate
to the nearest hundredth.
Step 1: Find the value of the whole number.
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.
3-6 Estimating Square Roots
Additional Example 3 Continued
Approximate
to the nearest hundredth.
Step 2: Find the value of the decimal.
Find the difference between the given
141 – 121 = 20 number, 141, and the lower perfect
square.
Find the difference between the
144 – 121 = 23 greater perfect square and the lower
perfect square.
20
Write the difference as a ratio.
23
Divide to find the approximate
20  3 ≈ 0.869 decimal value.
3-6 Estimating Square Roots
Additional Example 3 Continued
Approximate
to the nearest hundredth.
Step 3: Find the approximate value.
11 + 0.869 = 11.869
11.869 ≈ 11.87
Combine the whole number and
decimal.
Round to the nearest hundredth.
The approximate value of
hundredth is 11.87.
to the nearest
3-6 Estimating Square Roots
Check It Out: Example 3
Approximate
to the nearest hundredth.
Step 1: Find the value of the whole number.
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.
3-6 Estimating Square Roots
Check It Out: Example 3 Continued
Approximate
to the nearest hundredth.
Step 2: Find the value of the decimal.
Find the difference between the given
240 – 225 = 15 number, 240, and the lower perfect
square.
Find the difference between the
256 – 225 = 31 greater perfect square and the lower
perfect square.
15
Write the difference as a ratio.
31
Divide to find the approximate
15  31 ≈ 0.484 decimal value.
3-6 Estimating Square Roots
Check It Out: Example 3 Continued
Approximate
to the nearest hundredth.
Step 3: Find the approximate value.
15 + 0.484 = 15.484
15.484 ≈ 15.48
Combine the whole number and
decimal.
Round to the nearest hundredth.
The approximate value of
hundredth is 15.48.
to the nearest
3-6 Estimating Square Roots
Additional Example 4: Using a Calculator to Estimate
the Value of a Square Root
Use a calculator to find
the nearest tenth.
Using a calculator,
Rounded,
600. Round to
600 ≈ 24.49489742….
600 is 24.5.
3-6 Estimating Square Roots
Check It Out: Example 4
Use a calculator to find
the nearest tenth.
Using a calculator,
Rounded,
800. Round to
800 ≈ 28.2842712….
800 is 28.3.
3-6 Estimating Square Roots
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
3-6 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
3-6 Estimating Square Roots
Lesson Quiz for Student Response Systems
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
3-6 Estimating Square Roots
Lesson Quiz for Student Response Systems
2. Use a calculator to round to the nearest
tenth.
A. 2.3
B. 4.5
C. 6.7
D. 9.2
3-6 Estimating Square Roots
Lesson Quiz for Student Response Systems
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