Prove that 4 - 5√3 is an irrational number

Rational numbers are integers that are expressed in the form of p / q where p and q are both co-prime numbers and q is non zero.

Answer: Hence proved that 4 - 5√3 is an irrational number

Let's find if  4 - 5√3 is irrational

Explanation:

To prove that 4 - 5√3 is an irrational number, we will use the contradiction method.

Let us assume that 4 - 5√3 is a rational number with p and q as co-prime integers and q ≠ 0

⇒ 4 - 5√3 = p / q

⇒ 5√3 = 4 - p / q

⇒ √3 = (4q - p) / 5q

⇒ (4q - p) / 5q is a rational number

However, √3 is in irrational number

This leads to a contradiction that 4 - 5√3 is a rational number

Thus, 4 - 5√3 is an irrational number by contradiction method.