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September 2 - Radicals

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-5 + 19 4 (-5)-9 6 -3(9)-11(-5) 52/-4-16/-4 The symbol used to indicate a root is the radical symbol - Roots and Radicals Every radical expression has three ... – PowerPoint PPT presentation

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Title: September 2 - Radicals


1
September 2 - Radicals
  • -5 19
  • 4 (-5)
  • -9 6
  • -3(9)
  • -11(-5)
  • 52/-4
  • -16/-4

2
  • Roots and Radicals

The symbol used to indicate a root is the radical
symbol -
3
  • Roots and Radicals

Every radical expression has three parts
  • Radical symbol
  • Index
  • Radicand

4
  • Roots and Radicals

Every radical expression has three parts
5
  • Roots and Radicals

By convention, an index of 2 is not written since
it is the smallest possible index.
6
  • Roots and Radicals

The square root of 49 could be written as

but is normally written as .
7
  • Roots and Radicals

Example
because
Also
because
8
  • Roots and Radicals

Example
has two answers
7 is called the positive or principal square root.
-7 is called the negative square root.
9
Simplify
2
4
5
This is a piece of cake!
10
12
10
Estimating 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
11
Estimating 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.

12
Estimate to the Nearest Integer
5 -8 7 -5
  • v27
  • -v72
  • v50
  • -v22

13
Rational vs. Irrational
  • How are they alike?
  • Real Numbers
  • Can be decimals

14
Rational vs. Irrational
  • Rational
  • 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

15
Identifying 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

16
One and Done
  • is between which two integers?
  • What are the two square roots of 81?
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