Question

prove that √5-7 is irrational number​

Answer 1

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.Read more on Sarthaks.com - https://www.sarthaks.com/2956/prove-that-7-root-5-is-an-irrational-number