Question

prove that 2+√3/5 is irrational​

Answer 1

let 2+√3/5 is rational then

2+√3/5=p/q

here p and q are integers and co-prime to each other.

so

2+√3/5=p/q

(10+√3)/5=p/q

10+√3=5p/q

√3=(5p/q)-10

√3=(5p-10q)/q

as p and q are Integers

(5p-10q)/q will be a rational number

but it is equal to√3 which is irrational

which is not possible

so our assumption is wrong

therefore 2+√3/5 is irrational.

thanks for asking