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