Question

Prove that 3+root 7 is irrational.

Answer 1

3 + √7  >
LET  3 + √7 BE RATIONAL 
THEREFORE 3 +√7  =  P/Q WHERE P AND Q ARE COPRIMES AND Q≠0
3 +√7 = P/Q
√7  =  P-3Q/Q  (BY TAKING L.C.M)
BUT √7 IS IRRATIONAL AND P-3Q/Q IS RATIONAL 
THEREFORE L.H.S ≠ R.H.S 
THIS MEANS OUR CONTRADICTION WAS WRONG 3 + √7 IS IRRATIONAL ..