Question

prove that 2 minus root 3 is irrational given that root 3 is irrational​

Answer 1

Answer:

Given 3 is irrational number

Let 2-3 is rational number.

then 2-3=qp

3=qp+2q

Since 3 is irrational number but qp+2q is rational it mean 

irrational = rational

which contradict,

∴ our assumption is wrong and

2-3 is irrational number.

Answer 2

Let 2-root 3 = a/b (which is irrational)
And root 3= a/b+2 (as LHS is irrational which is given RHS is also irrational )
Hence proven