Question

Under what conditions are we allowed to add or subtract radicals together?

Answer 1

The radicals must be the same. if the indices or radicands are not the same, then you can NOT add or subtract the radicals

Answer 2

Answer/Step-by-step explanation:

The conditions where we are allowed to subtract or add radicals together is when the radicands, which is the number inside the radical, of both radicals are the same. And also, when they both have the same indices, that is, for example, they have the same root.

Take for example the following radical expression:

$4\sqrt{2} + 3\sqrt{2}$

Both radicals, $4\sqrt{2} and 3\sqrt{2}$, have the same radicand, $\sqrt{2}$ , and also the same index of square root.

Therefore, they are regarded as like terms, and can be added or subtracted together.

Thus,

$4\sqrt{2} + 3\sqrt{2} = 7\sqrt{2}$