SOLUTION: Classify the given numbers as real and rational, real and irrational, or complex. Remember to simplify BEFORE you classify! a. {{{(3)^(1/2) + 2i}}} b. {{{3.14}}} c. {{{pi}}}

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Classify the given numbers as real and rational, real and irrational, or complex. Remember to simplify BEFORE you classify! a. {{{(3)^(1/2) + 2i}}} b. {{{3.14}}} c. {{{pi}}}      Log On

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Question 196555This question is from textbook
: Classify the given numbers as real and rational, real and irrational, or complex. Remember to simplify BEFORE you classify!
a. %283%29%5E%281%2F2%29+%2B+2i
b. 3.14
c. pi
d. 16%5E%281%2F4%29+%2B+6
e. %2818%29%5E%281%2F3%29
Please help me. I don't understand this at all. This question is from textbook

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


A rational number is a number equal to a common fraction,
whether proper of improper.

a. %283%29%5E%281%2F2%29+%2B+2i 

sqrt%283%29+%2B+2i

This is complex because after simplifying it 
contains an "i".


b. 3.14

This can be written as 3.14%2F1, and
we can multiply top and bottom by 100 and
get rid of the edcimal. So we have

314%2F100

which reduces to 157%2F50 which is a 
common fraction, so it is rational.

c. pi

This is not equal to any common fraction, but
doesn't contain any i so it's irrational.

You should note here that pi is NOT equal
to 3.14.  The RATIONAL NUMBER 3.14
is only an approximation for pi.

d. 16%5E%281%2F4%29+%2B+6 
   root%284%2C16%29%2B6
   root%284%2C2%5E4%29%2B6
   2%2B6
   8

Since 8 can be written as the common fraction
8%2F1 it is rational.  
   
e. %2818%29%5E%281%2F3%29
   root%283%2C18%29

This cannot be simplified further, and it is not equal
to any common fraction, but doesn't contain any i,
so it's irrational.  

Edwin