Transcript 4-7 Estimating Square Roots Preview Evaluating Algebraic Expressions Warm Up California Standards Lesson Presentation 4-7 Estimating Square Roots Warm Up Evaluating Algebraic Expressions Find the two square roots of each number. 1.

4-7 Estimating Square Roots
Preview
Evaluating Algebraic Expressions
Warm Up
California Standards
Lesson Presentation
4-7 Estimating Square Roots
Warm
Up
Evaluating
Algebraic Expressions
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
4-7 Estimating Square Roots
California
Evaluating
Algebraic Expressions
Standards
NS2.4 Use the inverse relationship between
raising to a power and extracting the root of a
perfect square integer; for an integer that is not
a square, determine without a calculator the
two integers between which its square root
lies and explain why.
4-7 Estimating Square Roots
Additional Example 1: Estimating Square Roots of
Numbers
TheEvaluating
55 is between
two integers.
Name the
Algebraic
Expressions
integers. Explain your answer.
55
36, 49, 64, 81 List perfect squares near 55.
49 < 55 < 64
Find the perfect squares nearest 55.
49 < 55 < 64 Find the square roots of the perfect
squares.
7 < 55 < 8
55 is between 7 and 8 because 55 is between
49 and 64.
4-7 Estimating Square Roots
Check It Out! Example 1
The 80 is between two integers. Name the
Evaluating Algebraic Expressions
integers. Explain your answer.
80
49, 64, 81, 100 List perfect squares near 80.
64 < 80 < 81
Find the perfect squares nearest 80.
64 < 80 < 81 Find the square roots of the perfect
squares.
8 < 80 < 9
80 is between 8 and 9 because 80 is between
64 and 81.
4-7 Estimating Square Roots
Additional Example 2: Recreation Application
A Coast Guard boat searching for a lost sailboat
covers
a square area
of 185 mi2Expressions
. What is the
Evaluating
Algebraic
approximate length of each side of the square
area? Round your answer to the nearest mile.
The length of each side of the square is √185 .
144, 169, 196, 225
List perfect squares near 185.
169 < 185 < 196
Find the perfect squares nearest 185.
√169 < √185 < √196 Find the square roots of the perfect
squares.
13 < √185 < 14
185 is closer to 196 than to 169, so
√185  14
185 is closer to 14 than 13.
Each side of the search area is about 14 miles long.
4-7 Estimating Square Roots
Check It Out! Example 2
A tent was advertised in the newspaper as having
2. What is the
an enclosed
square
area
of
168
ft
Evaluating Algebraic Expressions
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
. near 168.
121, 144, 169, 196
List perfect squares
144 < 168 < 169
Find the perfect squares nearest 168.
√144 < √168 < √169 Find the square roots of the perfect
squares.
12 < √16 < 13
8
168 is closer to 169 than to 144, so
√168  13
168 is closer to 13 than 12.
Each side of the tent is about 13 feet long.
4-7 Estimating Square Roots
Additional Example 3: Approximating Square Roots
to the Nearest Hundredth
Evaluating
Expressions
Approximate
√135 Algebraic
to the nearest
hundredth.
Step 1 Find the value of the whole number.
121 < 135 < 144
Find the perfect squares nearest 135.
√121 < √135 <√ 144 Find the square roots of the perfect
squares.
11 < √ 135 < 12 The number will be between 11 and
12.
The whole number part of the answer is 11.
4-7 Estimating Square Roots
Additional Example 3 Continued
Approximate
√135 Algebraic
to the nearest
hundredth.
Evaluating
Expressions
Step 2 Find the value of the decimal.
Find the difference between the
135 – 121 = 14
given number, 135, and the lower
perfect square.
Find the difference between the
144 – 121 = 23
greater perfect square and the
lower perfect square.
14
Write the difference as a ratio.
23
Divide to find the approximate
14 ÷ 23 ≈ 0.609
decimal value.
4-7 Estimating Square Roots
Additional Example 3 Continued
Approximate
√135 Algebraic
to the nearest
hundredth.
Evaluating
Expressions
Step 3 Find the approximate value.
11 + 0.609 = 11.609 Combine the whole number and
decimal.
11.609 ≈ 11.61
Round to the nearest hundredth.
The approximate value of
is 11.61.
135 to the nearest hundredth
4-7 Estimating Square Roots
Check It Out! Example 3
Approximate
√180 Algebraic
to the nearest
hundredth.
Evaluating
Expressions
Step 1 Find the value of the whole number.
169 < 180 < 196
Find the perfect squares nearest
180.
√169 < √180 <√ 196 Find the square roots of the perfect
squares.
13 < √ 180 < 14 The number will be between 13 and
14.
The whole number part of the answer is 13.
4-7 Estimating Square Roots
Check It Out! Example 3 Continued
Approximate
√180 Algebraic
to the nearest
hundredth.
Evaluating
Expressions
Step 2 Find the value of the decimal.
Find the difference between the
180 – 169 = 11
given number, 180, and the lower
perfect square.
Find the difference between the
196 – 169 = 27
greater perfect square and the lower
perfect square.
11
Write the difference as a ratio.
27
11 ÷ 27 ≈ 0.407
Divide to find the approximate
decimal value.
4-7 Estimating Square Roots
Check It Out! Example 3 Continued
Approximate
√180 Algebraic
to the nearest
hundredth.
Evaluating
Expressions
Step 3 Find the approximate value.
13 + 0.407 = 13.407 Combine the whole number and
decimal.
13.407 ≈ 13.41
Round to the nearest hundredth.
The approximate value of
is 13.41.
180 to the nearest hundredth
4-7 Estimating Square Roots
Additional Example 4: Using a Calculator to
Estimate the Value of a Square Root
Evaluating Algebraic Expressions
Use a calculator to find
the nearest tenth.
600. Round to
600 ≈ 24.494897…
Use a calculator.
600 ≈ 24.5
Round to the nearest tenth.
600 rounded to the nearest tenth is 24.5.
4-7 Estimating Square Roots
Check It Out! Example 4
Evaluating
Algebraic
Expressions
Use a calculator to find 800. Round to
the nearest tenth.
800 ≈ 28.28427125… Use a calculator.
800 ≈ 28.3
Round to the nearest tenth.
800 rounded to the nearest tenth is 28.3.
4-7 Estimating Square Roots
Lesson Quiz
Each square root is between two integers.
Name
the integers.
Evaluating
Algebraic Expressions
1.
27
5 and 6
3. Approximate
13.75
2.
456
21 and 22
189 to the nearest hundredth.
4. Use a calculator to find
nearest tenth. 34.9
1219. Round to the
5. A square room requires 154 ft2 of wall-to-wall
carpeting to cover the floor. What is the length
of each side of the room? Round your answer
to the nearest foot. 12 ft