Question

help me pleaseeeeeeeeeeFor the drop box we havethe result is (rational/irrational)because it (cannot/can)be written as the ratio of two integers and it’s decimal expansion (does/does not) terminate or repeat.

Answer 1

Solution

We want to add

$3\sqrt[]{2}+\sqrt[]{10}$

Solution

We will notice the like terms and then factorise

$\begin{gathered} 3\sqrt[]{2}+\sqrt[]{10} \\ =3\sqrt[]{2}+\sqrt[]{5\times2} \\ =3\sqrt[]{2}+\sqrt[]{5}(\sqrt[]{2}) \\ =(3+\sqrt[]{5})\sqrt[]{2} \end{gathered}$

Therefore,

$\operatorname{Re}sult=(3+\sqrt[]{5})\sqrt[]{2}$