Question

Explain why only like radicals can be added or subtracted while unlike radicals can be multiplied or divided, Under what conditiones can unlike radicals not be multiplied on divided?

Answer 1

To multiply radicals with different indices, we need to find a common denominator, which is the lowest common multiple (LCM) between the roots. Once we obtain the LCM, we can multiply each root and exponent in the radicand to obtain the LCM, and rewrite as one radical

When we multiply two radicals with the same type of root (both square roots, both cube roots, and so on), we simply multiply the radicands (the expressions under the radical signs) and put the product under a radical sign