Question

prove that 7×√5 is an irrational number.​

Answer 1

Answer:

Step-by-step explanation:

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.