Answer:
Two irrational numbers such that when you add them gives you a rational number could be [tex]\sqrt{5}[/tex] and [tex]-\sqrt{5}-2[/tex].
The result when adding these is -2 which is a rational number.
(There are infinitely many examples.)
Step-by-step explanation:
How about opposite irrational numbers?
The sum of opposite numbers, no matter the classification of that number, is 0.
So examples:
[tex]2\sqrt{3}+-2\sqrt{3}=0[/tex]
[tex]\pi+(-\pi)=0[/tex]
[tex]-\sqrt{2}+\sqrt{2}=0[/tex]
If you wanted some more examples that have a sum other than 0:
[tex](\sqrt{3})+(-\sqrt{3}+1)=1[/tex]
[tex](\pi-1)+(-\pi+4)=3[/tex]
There are infinite amount of examples of the sum of two irrational numbers being a rational.
My last example: Two irrational numbers such that when you add them gives you a rational number could be [tex]\sqrt{5}[/tex] and [tex]-\sqrt{5}-2[/tex].
The result when adding these is -2 which is a rational number.
