Question

prove that the 7root5 is irrational ​

Answer 1

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.