Answer:
No, irrational numbers are not closed under addition.
Step-by-step explanation:
The closure property of irrational numbers under addition states that the sum of two irrational number will always be an irrational number.
That is if a and b are two irrational numbers then, their sum a + b should always be irrational.
Irrational numbers are not closed under addition.
This can be explained with the help of an example:
We know that [tex]\sqrt2[/tex] and [tex]-\sqrt2[/tex] are two irrational number.
If we consider their sum, then,
[tex]\sqrt2 + (-\sqrt2) = \sqrt2 - \sqrt2 = 0[/tex]
But 0 is a rational number.
Hence, irrational number are not closed under addition.
