show 7-√5 is irrational no.
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
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.