Question

Prove that root2+ root3 is irrational​

Answer 1

Answer:

Step-by-step explanation:

Squaring both sides, we have

2 + 2 \sqrt{6} + 3 = \: {r}^{2}

which means that ,

\sqrt{6} = {r}^{2} - 5

Since the set of rational numbers is closed under multiplication and addition,.

{r}^{2} - 5

is therefore rational. However, as we know /have proved earlier that √6  is an irrational. A contradiction!

Therefore, root2 +root3 is irrational.