Prove that 3+root 7 is irrational.
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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 ..
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 ..
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