Question

Is the sum of 3 square root of 2 and 4 square root of 2 rational or irrational

Answer 1

$3\cdot\sqrt[]{2}+4\cdot\sqrt[]{2}$

To solve we can take common factor the root of 2

$\begin{gathered} \sqrt[]{2}\cdot(3+4) \\ 7\cdot\sqrt[]{2} \end{gathered}$

We can see that when simplifying the sum the value of the root of 2 still remains. The root of 2 is irrational so the sum remains IRRATIONAL