Question

prove the 5+ 3√3 is a irrational no give that
√3 is a irrational no​

Answer 1

let us assume that 5 + 3√3 is rational number.

so, 5 + 3√3 = p/q [ where p and q are coprime integers and q not equal to 0 ]

(5 + 3√3 ) = p/q

√3 = p/3q -5

p/3q -5 is rational number so √3 is rational number but we have √3 is irrational no , so p/3q -5 is irrational no.

This contradicts our assumption so 5 + 3√3 is irrational no.