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Chapter 11, Section 1: Square Root and Irrational Numbers
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Warm UpSimplify:
7² =
3.5² =
15² =
0.4² =
49
12.25
225
0.16
Chapter 11, Section 1
Square Roots and Irrational Numbers
By Ms. Dewey-Hoffman
Area of a Square
The area of a square is the SQUARE of the length of a side. (s²)
The square of an integer is a perfect square.
Example: 2² = 4 (4 is a perfect square)4² = 16 (16 is a perfect square)
Everything in Math has an Opposite
The opposite of a SQUARE is a SQUARE ROOT.
The symbol: √ indicates a NONNEGATIVE Square Root of a number.Square Root = Radical
Same thing!!!
Examples
Simplify each Square Root:
√64 = ?
-√121 = ?
√100 = ?
-√16 = ?
8
-11
10
-4
13 Perfect Squares
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, and 144.
Recommend Memorizing.
Estimating Non-Perfect Squares
For Integers that are NOT perfect squares, you can estimate a square root.
√4 √9
2 2.5 3
√8 = 2.83
Estimating Square Roots to the Nearest Integer.
√15 → Look for the two perfect squares on either side of 15.
√9 < √15 < √16 → 15 is closer to 16.
√16 = 4Square root of 15 is close to 4.
√15 ≈ 4√15 = 3.87...
Estimate to the Nearest Integer
√27 =
-√72 =
√50 =
-√22 =
5
-8
7
-5
Classifying Real Numbers
RATIONAL Numbers as the RATIO of two integers: decimals and fractions.
But the decimal either repeats or terminates.
IRRATIONAL Numbers CANNOT be expressed as a ratio and NEITHER repeat nor terminate.
Positive Integer not a Perfect Square?Then the square root is irrational.
Identifying Rational or Irrational√18 = irrational, 18 not a perfect square
√121 = rational, 121 is a perfect square
-√24 = irrational, 24 not a perfect square
432.8 = rational, terminating decimal
0.1212... = rational, repeating decimal
0.120120012... = irrational
π = irrational
Identify Each
√2 = rational or irrational
-√81 = rational or irrational
0.53 = rational or irrational
√42 = rational or irrational
Assignment #30
Pages 562-563:
2-34 even #s, 39-45 all.
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