Transcript 8.NS.2 powerpoint_estimatingsquareroots

4-7 Estimating Square Roots
fact: Expressions
Evaluating Math
Algebraic
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
4-7 Estimating Square Roots
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
Example 2: 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
Example 2 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
Example 2 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
Example 3: 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.