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. Prove that √ 5 is an irrational number. Hence, show that -3 + 2√ 5 is an irrational number. Let us consider √ 5 be a rational number, then √ 5 = p/q, where ‘p’ and ‘q’ are integers, q 0 and p, q have no common factors (except 1). So, 5 = p 2 / q 2 p 2 = 5q 2 …. (1) As we know, ‘ 5 ’ divides 5q 2, so ‘ 5 ’ divides p 2 as well. Theorem 10.4 Prove that √2 is irrational . We have to prove √2 is irrational Let us assume the opposite, i.e., √2 is rational Hence, √2 can be written in the form 𝑎/𝑏 where a and b (b≠ 0) are co-prime (no common factor other than 1) Hence, √𝟐 = 𝒂/𝒃 √2 b = a Squa Prove that 2 + 3 5 is an irrational number , given that 5 is an irrational number .
