11.1 square root irrational
DESCRIPTION
Chapter 11, Section 1: Square Root and Irrational NumbersTRANSCRIPT
![Page 1: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/1.jpg)
Warm UpSimplify:
7² =
3.5² =
15² =
0.4² =
49
12.25
225
0.16
![Page 2: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/2.jpg)
Chapter 11, Section 1
Square Roots and Irrational Numbers
By Ms. Dewey-Hoffman
![Page 3: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/3.jpg)
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)
![Page 4: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/4.jpg)
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!!!
![Page 5: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/5.jpg)
Examples
Simplify each Square Root:
√64 = ?
-√121 = ?
√100 = ?
-√16 = ?
8
-11
10
-4
![Page 6: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/6.jpg)
13 Perfect Squares
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, and 144.
Recommend Memorizing.
![Page 7: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/7.jpg)
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
![Page 8: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/8.jpg)
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...
![Page 9: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/9.jpg)
Estimate to the Nearest Integer
√27 =
-√72 =
√50 =
-√22 =
5
-8
7
-5
![Page 10: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/10.jpg)
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.
![Page 11: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/11.jpg)
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
![Page 12: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/12.jpg)
Identify Each
√2 = rational or irrational
-√81 = rational or irrational
0.53 = rational or irrational
√42 = rational or irrational
![Page 13: 11.1 Square Root Irrational](https://reader035.vdocuments.net/reader035/viewer/2022081717/55556e49b4c9055f5f8b47d9/html5/thumbnails/13.jpg)
Assignment #30
Pages 562-563:
2-34 even #s, 39-45 all.