Question

Prove that 7- root 5 is an irrational number

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.