why do we need to rationalize denominators?

Question

i dont want to know how-i already know how to do that-i need to know why

Answer 1

James has mentiioned the reason for consatants. easy for calculation but this is done for polynomial and constants in a different reason this is a simple approach to add or do any operation. In some cases it simpifies also

for example

(1/sqrt(3) - 1/sqrt(2)
this how do I calulate

sqrt(3)/3 - sqrt(2)/2 = 2sqrt(3) - 3 sqrt(2)/6
this is easy

I could have caluclated in other way but cumbersom

I

Answer 2

Actually, there is a practical reason that inspired this convention.

Consider these two equivalent expressions, 1/sqrt(2) and sqrt(2)/2.

Suppose you wanted to compute the value of either of these expressions, without using a calculator. Your choice is to compute

1 / 1.4142135...

or

1.4142135... / 2

Now imagine computing either of these quotients using long division. Which do you think would be easier?

Answer 3

I believe it does not really matter, but that some teachers think it is "cleaner" to do so.

Answer 4

it's the convention ...