Math fact:
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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Math fact: Math fact: The sum of any number of The sum of any number of consecutive odd whole numbers, consecutive odd whole numbers, beginning with 1, is a perfect beginning with 1, is a perfect square square e.g. 1+3=4, 1+3+5=9, 1+3+5+7=16 e.g. 1+3=4, 1+3+5=9, 1+3+5+7=16
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Math fact: The sum of any number of consecutive odd whole numbers, beginning with 1, is a perfect square e.g. 1+3=4, 1+3+5=9, 1+3+5+7=16. 55. 55 is between 7 and 8 because 55 is between 49 and 64. 49 < 55 < 64. 7 < 55 < 8. Example 1: Estimating Square Roots of Numbers. - PowerPoint PPT Presentation
Transcript of Math fact:
Evaluating Algebraic Expressions
4-7 Estimating Square Roots
Math fact:Math fact:
The sum of any number of The sum of any number of consecutive odd whole numbers, consecutive odd whole numbers,
beginning with 1, is a perfect squarebeginning with 1, is a perfect square
e.g. 1+3=4, 1+3+5=9, 1+3+5+7=16e.g. 1+3=4, 1+3+5=9, 1+3+5+7=16
Evaluating Algebraic Expressions
4-7 Estimating Square RootsExample 1: Estimating Square Roots of Numbers
The 55 is between two integers. Name the integers. Explain your answer.
List perfect squares near 55.36, 49, 64, 81
49 < 55 < 64
Find the square roots of the perfect squares.
55
55 is between 7 and 8 because 55 is between 49 and 64.
Find the perfect squares nearest 55.
49 < 55 < 64
7 < 55 < 8
Evaluating Algebraic Expressions
4-7 Estimating Square RootsExample 2: Approximating Square Roots to the Nearest
Hundredth
121 < 135 < 144
The whole number part of the answer is 11.
Find the perfect squares nearest 135.
Find the square roots of the perfect squares.
√121 < √135 < 144√
11 < 135 < 12√
Step 1 Find the value of the whole number.
The number will be between 11 and 12.
Approximate √135 to the nearest hundredth.
Evaluating Algebraic Expressions
4-7 Estimating Square RootsExample 2 Continued
135 – 121 = 14
14 ÷ 23 ≈ 0.609
Find the difference between the given number, 135, and the lower perfect square.
Approximate √135 to the nearest hundredth.
Step 2 Find the value of the decimal.
Write the difference as a ratio.
144 – 121 = 23Find the difference between the greater perfect square and the lower perfect square.
1423
Divide to find the approximate decimal value.
Evaluating Algebraic Expressions
4-7 Estimating Square RootsExample 2 Continued
11 + 0.609 = 11.609 Combine the whole number and decimal.
Step 3 Find the approximate value.
11.609 ≈ 11.61 Round to the nearest hundredth.
The approximate value of 135 to the nearest hundredth is 11.61.
Approximate √135 to the nearest hundredth.
Evaluating Algebraic Expressions
4-7 Estimating Square RootsExample 3: Using a Calculator to Estimate the Value of a
Square Root
Use a calculator to find 600. Round to the nearest tenth.
600 ≈ 24.5
600 ≈ 24.494897… Use a calculator.
Round to the nearest tenth.
600 rounded to the nearest tenth is 24.5.
