Question

Prove that 4-3 is an irrational number

Answer 1

Let root 4-root 3 be a rational number
Root 4-root 3=p/q(where p and q are rational nos, q is not equal to 0 and both are Co prime)
By squaring both the sides we get,
4+3-(4)*root 6=p^2/q^2
So (4)*root 6= -(p^2/q^2)+7
If p/q is a rational no then -(p^2/q^2)+7 is also a rational no but it contradicts that (4)*root 6 is a rational no
So root 4-root 3 is an irrational no

Answer 2

Answer::

Given that(4-√3) is irrational number.

Let (4-√3) is rational number.

Where p/q are co- prime and q doesn't equal to 0.

4- √3=p/q

√3=p/q+4

√3=p+4q/q

We know that√3 is irrational number,

while RHS is in p/q form.

Therefore,LHS=RHS

So,Our assumption was wrong.

Hence,4-√3 is irrational number.