Prove that 2sqrt2 is irrational number. | Discrete Structure 2080

Discrete Structure20805 marksProof by contradiction

Prove that $2\sqrt{2}$ is irrational number. [5]

A rational number is any number that can be expressed as $\frac{p}{q}$ , where $p, q \in \mathbb{Z}$ and $q \neq 0$ , with $\gcd(p, q) = 1$ . - An irrational number is a number that cannot be expressed in such a form. --- Assume, for the sake of contradiction, that $2\sqrt{2}$ is rational. Then, b...

A rational number is any number that can be expressed as $\frac{p}{q}$, where $p, q \in \mathbb{Z}$ and $q \neq 0$, with $\gcd(p, q) = 1$. - An irrational number is a number that cannot be expressed in such a form. --- Assume, for the sake of contradiction, that $2\sqrt{2}$ is rational. Then, b...