Question

prove that root 2 +3 root is irrational

Answer 1

Answer:

Let 2+√3 is a rational number

we know that a number Which is in the form of p/q where p and q is a integers and q not equl to 0

2+√3=p/q

√3=p/q-2

Lcm of q is q

√3=p-2q/q

squaring both side get

(√3)²=(p-2q)²/q*q

3q=(p-2q)²/q-----------------(1)

in eq^n 1 3q is a integers and (p-2q)²/q is a fraction and we know that integers not equal to fraction

So 2+√3 is irrational number