Question

7+√5 prove that irrational

Answer 1

LET US ASSUME THAT 7 + √5 IS RATIONAL NUMBER

∴ 7 + √5 = a/b (a and b are integers)

√5 = a/b − 7

√5 = a-7b/b

IF a,b ARE INTEGERS THEN a-7b/b IS RATIONAL NUMBER.

SO √5 IS ALSO A RATIONAL NUMBER. BUT THIS CONTRADICTS THE FACT THAT √2 IS IRRATIONAL.

∴ WE CONCLUDE THAT 7 + √5 IS IRRATIONAL NUMBER.

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