Question

Prove that 2-√3 is irrational, given that √3 is irrational.

Answer 1

Answer:Let 2+√3 be a rational number.

So, 2+√3 = a/b

√3 = a/b -2

a/b is a rational number and 2 is a rational number. We know that Rational number- rational number= Rational number. So, a/b -2 is rational.

But √3 is irrational.

This contradicts the fact that rational≠ irrational.

So, our supposition is incorrect.

Hence, 2+√3 is an irrational number.

Step-by-step explanation:

Answer 2

Answer:

let 2-root 3 is rational no

Root3 =P/Q (Q not equal to 0 ) p and q are coprime

2-√3 = P/Q (2 is goes in +)

√3 = P+2q/q

√3 is irrational no = p+2q/q is rational no

it is contradiction irrotianal no. is not equal to rational no so 2-√3 is irrational no