Question

prove that √3+√4 is irrational number​

Answer 1

Answer:

Let us assume, to the contrary that √3+√4 is a rational number.

So, √3+√4=p/q where, q is not equal to 0 and p& q are co- primes i. e. p&q have H. C. F =1.

√3+√4=p/q

√3+√4q=p ----(1)

Squaring both sides

(√3+√4) ^2= (p) ^2

3+2√12+4 =p^2

7+2√12=p^2

2√12=p^2-7

√12=p^2-7/2

As you can clearly see that R. H. S is rational number but L. H. S. is irrational number.

But this contradicts the fact that √3+√4 is irrational.

This contradiction has arisen because of our incorrect assumption.