Question

prove that 1/3√3is irrational

Answer 1

here 1/3√3
= 1/3√3 ×√3/√3
= √3/9
you can write it this type
= √3×1/9
we know that product of a rational number and irrational number is always irrational .
so
1/3√3 is a irrational number.

Answer 2

Let us assume 1/3√3 as rational in the form of a/b,where a and b are positive integers and a and b ≠ 0
1/3√3=a/b⇒b=3√3×a⇒√3=b/3a=1/3(b/a)=a rational number
This tells that √3 is rational
But we know that √3 is irrational.
Hence,our assumption is wrong.
∴Hence,1/3√3 is irrational.