Question

prove that 3 +√7 is an irrational number​

Answer 1

$\large{\underline{\boxed{ Answer}}}$

Let 3 + √7 be a rational number then it can be expressed in the form of P/q where p and q are co-prime and q ≠ 0.

Then,

$\implies$ $3 + \sqrt{7} = \frac{p}{q}$

transfer 3 on R. H. S

$\implies$ $\sqrt{7} = \frac{p}{3q}$

we know that √7 is an irrational number.

also,every operation of a rational is itself a rational number.

Then, division of rational is also rational number.

but L. H. S is an irrational and R. H. S is rational

Therefore, L. H. S ≠ R. H. S

hence,our assumption is wrong 3+√7 is an irrational number