Can you add, subract, multiply, or divide two irrational numbers together?
Of course you can: for example sqrt(2), which is an irrational number. You can add, subtract, divide and multiply it by another irrational number such as Pi(3.141592653......etc.), which is also an irrational number.
I'll just do some examples
\(\sqrt2+\sqrt3\qquad \mbox{Cannot be simplified}\\ \sqrt2-\sqrt3\qquad \mbox{Cannot be simplified}\\ \sqrt2*\sqrt3=\sqrt{2*3}=\sqrt6\\ \sqrt2\div\sqrt3=\frac{\sqrt2}{\sqrt3}=\sqrt{\frac{2}{3}}\)
Although the first two cannot be simplified they are still added together. :)
You can approximate a single number answer if you want to.