CPhill

All whole numbers are rational

Not all real numbers are rational  ....."pi" is an example

Example of an imaginary number.......   sqrt(-36)  = 6i

Sorry.....GenericUsernameHere.....I didn't see the "tilde"

This means "congruent"    ....in other words, the two things on either side of the congruency sign have the same size and shape......

2n² = -144     divide by 2 on both sides

n² = -72       take the positive and negative roots of both sides

n = (plus/minus)sqrt(-72)

n = (plus/munus)( 6i ) * sqrt(2) 

This is known as the "reflexive" property

Here's a good resource that explains this :  http://www.purplemath.com/modules/sqrquad.htm

sqrt(9/16)  = 3/4

1/2+7x/10=13/20       multiply through by the common denominator of 2, 10 and 20, i.e., (20)

10 + 14x  = 13           subtract 10 from both sides

14x  = 3                     divide both sides by 14

x = 3/14

(1 + 1/4) * -(2 + 3/5) =

(5/4) * (-13/5)  =

(-13/4) * (5/5)  =

(-13/4) * (1)  =

-13/4

This is just a notational convention

ae(+/-)N    just means    a x 10^(+/-)N

If we have this :

(-9)⁴    the answer is  6561

If we have this :

-9⁴   the answer is -6561