Ex 1.2, 1 Prove that √ 5 ... Prove that 2 + 3 5 is an irrational number , given that 5 is an irrational number . Prove that √3 + √ 5 is irrational - Irrational numbers are those real numbers that cannot be represented in the form of a ratio. In other words, those real numbers that are not rational numbers are known as irrational numbers.√3 + √ 5 is irrational . Learn how to prove that root 5 is irrational using contradiction method, long division method, and examples. Find out the definition, properties, and examples of rational and irrational numbers.