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?