Question

Prove that 2+√3 is irrational.​

Answer 1

$\huge\mathfrak\red{Answer:}$

Rational numbers:

• Rational numbers are the numbers that can be written in the form of p/q where p and q are integers and q is not equal to zero.
• Example 2/3, 5/7, 9/7 etc.

Given:

• We have been given a number 2+√3.

To Prove:

• We need to prove that 2+√3 is irrational.

Solution:

Let us assume that 2+√3 is rational.

=> 2 + √3 = a/b

=> 2 - a/b = -√3

=> √3 = a/b - 2

=> √3 = a - 2b/b

But, a and b are positive integers therefore a - 2b/b is rational.

=>√3 is rational.

But this contradicts the fact that √3 is irrational.

Therefore, 2+√3 is irrational.

Hence proved!!