# example of irrational + irrational = rational

• Apr 3rd 2010, 06:54 AM
saha.subham
example of irrational + irrational = rational
plzz give me examples when two DIFFERENT irrational numbers add up to form a rational number.

a + b = c where a and b are two different irrational numbers and c is a rational numbers.

i will be very much helpful if i get more than one example. plzz help thanks in advance.
• Apr 3rd 2010, 07:16 AM
Sudharaka
Quote:

Originally Posted by saha.subham
plzz give me examples when two DIFFERENT irrational numbers add up to form a rational number.

a + b = c where a and b are two different irrational numbers and c is a rational numbers.

i will be very much helpful if i get more than one example. plzz help thanks in advance.

Dear saha,

Take any irrational number and it's negetive,

e.g; $\displaystyle a=\sqrt{2}~and~b=-\sqrt{2}$

Then, $\displaystyle \sqrt{2}-\sqrt{2}=0\in{Q}$

• Apr 3rd 2010, 08:09 AM
ICanFly
One more example:

$\displaystyle a=\sqrt{2}~and~b=1-\sqrt{2}$

$\displaystyle \sqrt{2}+1-\sqrt{2}=1\in{Q}$

• Apr 4th 2010, 03:44 AM
HallsofIvy
Quote:

Originally Posted by MJ*
hi earboth....i dont think so thats true..22/7 is an irrational number ;it is infact pi. (3.1411592...)

And if u ay that irrational numbers cant be expressed in form of fractions; then sqrt(2) wud not have been an irrtional number;coz it can be expressed in fractional form sqrt(2)/1

for reference see:
Pi - Wikipedia, the free encyclopedia

Normally I wouldn't get too rough with people who respond to questions they have no clue about but posting a reference to Wikipedia that you didn't even bother to read carefully yourself enrages me.

Wikipedia does NOT say that $\displaystyle \pi$ is equal to "22/7". It lists that as one of many rational approximations to $\displaystyle \pi$.

A number is rational if and only if it can be written as a fraction with integer numerator and denominator- that is often used as the definition of "rational number". Saying that $\displaystyle \sqrt{2}= \sqrt{2}{1}$ does NOT make it a rational number because the numerator is not an integer.

$\displaystyle \pi$ is irrational, 22/7 is rational. They are NOT equal, they are "close"- and not that very close. 22/7= 3.142857142857... and differs from $\displaystyle \pi$ in just the third decimal place.