Title: September 2 - Radicals
1September 2 - Radicals
- -5 19
- 4 (-5)
- -9 6
- -3(9)
- -11(-5)
- 52/-4
- -16/-4
2The symbol used to indicate a root is the radical
symbol -
3Every radical expression has three parts
4Every radical expression has three parts
5By convention, an index of 2 is not written since
it is the smallest possible index.
6The square root of 49 could be written as
but is normally written as .
7Example
because
Also
because
8Example
has two answers
7 is called the positive or principal square root.
-7 is called the negative square root.
9Simplify
2
4
5
This is a piece of cake!
10
12
10Estimating Non-Perfect Squares
- For Integers that are NOT perfect squares, you
can estimate a square root.
v8 2.83
v4
v9
2
2.5
3
11Estimating Square Roots to the Nearest Integer.
- v15 ? Look for the two perfect squares on either
side of 15. - v9 lt v15 lt v16 ? 15 is closer to 16.
- v16 4
- Square root of 15 is close to 4.
12Estimate to the Nearest Integer
5 -8 7 -5
13Rational vs. Irrational
- How are they alike?
- Real Numbers
- Can be decimals
14Rational vs. Irrational
- Whole numbers
- 1, 2, 3, 4
- Fractions ratio
- ½ , ¾
- Terminating decimal
- 5.25 5 1.05
- Repeating decimal
- 100 3 33.333
-
- Non-repeating, non-terminating decimal
- p 3.1415926
- Rounded, but not exact or predictable
- p 3.1416
15Identifying Rational or Irrational
- v18 irrational, 18 not a perfect square
- v121 rational, 121 is a perfect square
- -v24 irrational, 24 not a perfect square
- 432.8 rational, terminating decimal
- 0.1212... rational, repeating decimal
- 0.120120012... irrational
- p irrational
16One and Done
- is between which two integers?
- What are the two square roots of 81?