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Unformatted text preview: Chapter 10 Rational Exponents, Radicals,
and Complex Numbers 10.1 Radicals and Radical Functions The inverse of squaring a number is taking the square root of a number. A number 6 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. Principal and Negative Square Roots If a is a nonnegative number, then x/E is the principal or nonnegative square root
of a — a is the negative square root of a
A radical expression is an expression containing a radical Sign. A 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. Examples: V49 3L
\ w :NC‘TH m 23*
\i d \m 25 Z L
0x 'Jxv We R Li Jfé 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 irrational
numbers. ‘ IF REQUESTED , you can ﬁnd a decimal approximation for these irrational
numbers. Otherwise, leave them in radical form. Radicands might also contain variables and powers of variables. To avoid negative radicands, assume for this c hapter that if a variable appears in the
radicand, it represents positive numbers only. x I”) Cube Root yn . : X
The cube root of a real number a is written as Va— and \ﬂ / X
2 n 
yg=bonlyifb3=a is: 7 . n J  x
. X
\ Examples: V? = 3
&
il—Bx6 = m 9 X Other roots can be found, as well. The nth root of a is deﬁned as #5 = b only ifb" = a. 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. ' Simplify the following. biilallll‘l‘ll’l: 5 32a5'
_ — bIS = ...
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This note was uploaded on 01/16/2012 for the course MATH 096 taught by Professor Jimcotter during the Fall '11 term at Truckee Meadows Community College.
 Fall '11
 JimCotter

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