Prove that 3 + 2√5 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 3 + 2√5 is an irrational number
Let's find if 3 + 2√5 is irrational.
To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.
⇒ 3 + 2√5 = p/ q
⇒ 2√5 = p/ q - 3
⇒ √5 = (p - 3q ) / 2q
⇒ (p - 3q ) / 2 q is a rational number.
However, √5 is an irrational number
This leads to a contradiction that 3 + 2√5 is a rational number.
Thus, 3 + 2√5 is an irrational number by contradiction method.