Question

prove that root 3+2 is irrational

Answer 1

♥Hi friend♡

Let 2+√3 is a rational number.

A rational number can be written in the form of p/q.

2+√3=p/q

√3=p/q-2

√3=(p-2q)/q

p,q are integers then (p-2q)/q is a rational number.

But this contradicts the fact that √3 is an irrational number.

So,our supposition is false.

Therefore,2+√3 is an irrational number.

Hence proved.

♥Hope it helps♡

Answer 2

Step-by-step explanation:

a rational no. can be written in the form of p/q.

So,

$2 + \sqrt{3} = p \div q$

root 3 = p/q - 2

root 3 = (p-2q) / a

then , p and q are integers, then (p-2q) /q are rational numbers.

so this is a contradiction

Therefore, 2+ root 3 is a irrational number