Question

show that 7 minus root 5 is irrational given root 5 is irrational​

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 √5 IS IRRATIONAL.  

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