Question

28. When adding or subtracting like radicals, are the radicands added or
subtracted? Explain.

Answer 1

No, the radicands are not added.

Explanation:

When adding or subtracting like radicals, we treat them as we treat algebraic expressions:

4 x + x - 2 x= 3 x

In the sense that we associate the "x" above with the radical expression. So for example:

`4\,\sqrt[3]{x-7} \,+\,\sqrt[3]{x-7} -\,2\,\sqrt[3]{x-7} = (4+1-2)\,\sqrt[3]{x-7} =3\,\sqrt[3]{x-7}`

The radicals remain the same, and we treat them as algebraic expressions, just combining adequately the multiplicative factors the radicals have.