Question

prove √2+√3 is irrational number​

Answer 1

this is your answer

Answer 2

Step-by-step explanation

Let us assume that  $\sqrt{2}$ + $\sqrt{3$ are rational nos.

=>  $\sqrt{2}$ + $\sqrt{3$= p/q

squaring on both sides

=> 2 + 3 + 2$\sqrt{6}$ = $p^{2}$/$q^{2}$       { $(a+b)^{2}$ identity }

=> root6 =  $p^{2}$ - 6/2$q^{2}$

here LHS is irrational and RHS is rational.

therefore, LHS is not equal to RHS

=> our assumption is wrong

Therefore, $\sqrt{2}$ + $\sqrt{3$ is an irrational no.

                                                             HENCE PROVED