Question

example of some irrationals whose sum is a rational?

Answer 1

Heya,
Here is your answer.

- The sum of two irrrational numbers may be rational or irrational number.

Some examples where the sum of irrational numbers is rational

° √2+ √2= √4 =2, is a rational no.
° √61+ √39 = √100 = 10
° √3+√6= √9 = 3
° √10+√6=√16 =4
° √10+√15 = √25 = 5
° √30+√6=√36=6
°√9999+√1=√10000=100
° √39+√10=√49=7

Hope it helps..

Answer 2

Number system,

Defination: Irrational numbers are those numbers who's values are non terminating and non recurring in nature.

Like √2 if you find the value of this number you will find the value of this number as 1.4142135623.....
It's non terminating in nature and doesn't show any pattern.

So we can conclude that √2 is a Irrational number.
Similarly √3,√6,√7,√8,√10,.. are irrational numbers.Infact the numbers which are not perfect square numbers there root are irrational in nature.

Caution:√4√9 √16... are not irrational numbers they are rational numbers i.e.√4 = 2,√9 = 3,√16 = 4....

Now the addtion the irrational number as follows,

√2+√3 = √2+√3
and,√2+√2 = 2√2

So we can conclude that sum of irrational numbers are sometimes irrational.

Why sometimes ?
Patient, getting to that point

If we add √2 and -√2 the sum will be rational number,
√2 - √2 = 0 which is a rational number.
√3 -√3 = 0 and so on
So the sum of irrational numbers are sometimes rational also.

So the final conclusion is that tha sum if irrational numbers can be irrational as well as rational.

That's it
Hope it helped (ヽ´ω`)