Prove that root 5 is irrational: Learn how to use the method of

Learn how to use the method of contradiction to show that √ 5 is not a rational number. Follow the step-by-step proof with explanations and examples. 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 . 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 √ 5 is an irrational number and this can be proved by the method of contradicion. In this method, we first assume √ 5 to be rational, then we will show that it leads to contradiction which hence proves √ 5 to be irrational .