Question

Prove that 1/ root3
is irrational, given that root3 is irrational,​

Answer 1

Hii friend,

We have 1/✓3 = 1/✓3 × ✓3/✓3 = 1/3 × ✓3.... (1)

If possible, Let 1/✓3 be rational Number. Then , from (1) , 1/3×✓3 is rational Number.

Now, 3 is rational , 1/3×✓3 is rational.

=> 3 × 1/3 × ✓3 is also rational. [ Because product of two rationals is rational]

=> ✓3 is rational.

This contradicts the fact that ✓3 is irrational.

Since,

The contradiction arises by assuming that 1/✓3 is rational. So, 1/✓3 is irrational..... PROVED.......

HOPE IT HELPS UH :-)