proove that root 2 is a irrational number

1.	proove that root 2 is a irrational number
Answer» Let\xa0√2 be a rational number\xa0Therefore,\xa0√2= p/q [ p and q are in their least terms i.e., HCF of (p,q)=1 and q\xa0≠ 0On squaring both sides, we get p²= 2q² ...(1)Clearly, 2 is a factor of 2q²⇒ 2 is a factor of p² [since, 2q²=p²]⇒ 2 is a factor of p\xa0Let p =2 m for all m ( where m is a positive integer)Squaring both sides, we get p²= 4 m² ...(2)From (1) and (2), we get 2q² = 4m² ⇒ q²= 2m²Clearly, 2 is a factor of 2m²⇒ 2 is a factor of q² [since, q² = 2m²]⇒ 2 is a factor of q\xa0Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1 Therefore, Our supposition is wrongHence\xa0√2 is not a rational number i.e., irrational number.Read more on Brainly.in - https://brainly.in/question/2367037#readmore

Discussion