Given : 7 − √5

LET US ASSUME THAT 7 − √5 IS RATIONAL NUMBER

∴ 7 − √5 = a/b (a,b ∈ z , where b ≠ 0)

−√5 = a/b − 7

√5 = 7 − a/b

IF a,b ARE INTEGERS THEN 7 − a/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.