iwbat find and estimate square roots of numbers. · 2018. 9. 7. · 9-7 squares and square roots...
TRANSCRIPT
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9-7 Squares and Square Roots
IWBAT find and estimate square roots of
numbers.
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9-7 Squares and Square Roots
Vocabulary
perfect square
square root
radical sign
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9-7 Squares and Square Roots
2
Exponent
Base
A square with sides that measure 3 units each has an area of 3 · 3, or 32. Notice that the area of the square is represented by a power in which the base is the side length and the exponent is 2. A power in which the exponent is 2 is called a square.
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9-7 Squares and Square Roots
Find each square.
EX 1A: Finding Squares of Numbers
122
Method 1: Use a model.
A = lw
A = 12 · 12
A = 144
The square of 12 is 144.
12
12
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9-7 Squares and Square Roots
Find each square.
EX 1B: Finding Squares of Numbers
3.52
Method 2: Use a calculator.
Press 3.5
3.52 = 12.25
The square of 3.5 is 12.25.
x2 ENTER .
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9-7 Squares and Square Roots
WRITE:
A perfect square is the square of a whole number. The number 36 is a perfect square because 36 = 62 and 6 is a whole number.
The square root of a number is one of the two equal factors of the number. Four is a square root of 16 because 4 · 4 = 16. The symbol for a square root is √ , which is called a radical sign.
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9-7 Squares and Square Roots
√16 = 4 is read as “The square root of 16 is 4.”
Reading Math
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9-7 Squares and Square Roots
Find each square root.
The square root of 16 is 4.
√16
Method 1: Use a model.
EX 2A: Finding Square Roots of Perfect Squares
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9-7 Squares and Square Roots
Find each square root.
Press 676 .
The square root of 676 is 26.
x2 ENTER
EX 2B: Finding Square Roots of Perfect Squares
√676 Method 2: Use a calculator.
2nd
√676 = 26
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9-7 Squares and Square Roots
Estimate each square root to the nearest whole number. Use a calculator to check your answer.
EX 3A: Estimating Square Roots
36 < 40 < 49
Check
Find the perfect squares nearest 40.
Find the square roots of 36 and 49.
40 is closer in value to 36 than to 49.
6 is a reasonable estimate.
√36 < √40 < 49 √
6 < 40 < 7 √
40 6 √
40 6.32455532033 √ Use a calculator to approximate √40.
√40
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9-7 Squares and Square Roots
EX 3B: Estimating Square Roots
Estimate each square root to the nearest whole number. Use a calculator to check your answer.
64 < 79 < 81
Check
Find the perfect squares nearest 79.
Find the square roots of 64 and 81.
79 is closer in value to 81 than to 64.
√79
79 9 √
79 8.8881944 √
8 < 79 < 9 √
√64 < √79 < 81 √
Use a calculator to approximate √79.
9 is a reasonable estimate.
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9-7 Squares and Square Roots
A Coast Guard boat searching for a lost sailboat covers a square area of 125 mi2. What is the approximate length of each side of the square area? Round your answer to the nearest mile.
EX 4: Recreation Application
121 < 125 < 144 Find the perfect squares nearest 125.
Find the square roots of 121 and 144.
Each side of the search area is about 11 miles long.
125 is closer to 121 than to 144.
The length of each side of the square is √125 .
< < √125 √121 √144
11 < < 12 √125
√125 11