1 / 14

Section 7.1

Section 7.1. Radicals and Radical Functions. Square Roots. Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a if b 2 = a. In order to find a square root of a , you need a number that, when squared, equals a.

raheem
Download Presentation

Section 7.1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 7.1 Radicals and Radical Functions

  2. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a if b2 = a. In order to find a square root of a, you need a number that, when squared, equals a.

  3. Principal Square Roots Principal and Negative Square Roots If a is a nonnegative number, then is theprincipalor nonnegative squarerootof a and is the negative square rootof a.

  4. REVIEW: Perfect Squares 4 = 2264 = 82x2 = x • x 9 = 3281 = 92x4 = (x2 )2 16 = 42100 = 102x6 = (x3)2 25 = 52 121 = 112 36 = 62 144 = 122 49 = 72 169 = 132

  5. Radicands Radical expression is an expression containing a radical sign. Radicand is the expression under a radical sign. Note that if the radicand of a square root is a negative number, the radical is NOT a real number.

  6. Radicands Example:

  7. Perfect Squares Square roots of perfect square radicands simplify to rational numbers (numbers that can be written as a quotient of integers). Square roots of numbers that are not perfect squares (like 7, 10, etc.) are irrationalnumbers. IF REQUESTED, you can find a decimal approximation for these irrational numbers. Otherwise, leave them in radical form.

  8. Perfect Square Roots Radicands might also contain variables and powers of variables. To avoid negative radicands, assume for this chapter that if a variable appears in the radicand, it represents positive numbers only. Example:

  9. Cube Roots Thecube rootof a real number a is written as

  10. List of Perfect Cubes 8= 23 -8= (-2)3 27 = 33 -27 = (-3)3 64 = 43-64 = (-4)3 125 = 53-125 = (-5)3 216 = 63-216 = (-6)3 343 = 73-343 = (-7)3 512 = 83-512 = (-8)3

  11. Cube Roots Example:

  12. nth Roots Other roots can be found, as well. The nth rootof a is defined as If the index, n, is even, the root is NOT a real number when a is negative. If the index is odd, the root will be a real number.

  13. Power Card

  14. nth Roots Example: Simplify the following.

More Related