Question

are there two distinct irrational numbers such that their difference is a rational number? justify

Answer 1

Yes!
JUSTIFICATION :
$(2 + \sqrt{ 2)} - ( - 2 + \sqrt{2}) = 4$
4 is a rational number.
Hope that helps you ✌️

Answer 2

Answer:

$1+\sqrt2$ and $\sqrt2-1$ are two distinct irrational numbers such that their difference is a rational number.

Step-by-step explanation:

we have to justify that are there two distinct irrational numbers such that their difference is a rational number.

Let two irrational numbers are $1+\sqrt2$ and $\sqrt2-1$

Difference can be calculated as

$1+\sqrt2-(\sqrt2-1$)

⇒ $1+\sqrt2-\sqrt2+1=2$,which is a rational number.

Hence,  $1+\sqrt2$ and $\sqrt2-1$ are two distinct irrational numbers such that their difference is a rational number.