How to multiply radical expressions having the same indices?

Using the distributive property of multiplication over addition, when two radicals have the same index, we can multiply them by adding their exponents together. This is known as the radical exponentiation method. So, if we have two radical expressions with the same index and we want to find their product, we first need to find their sum of exponents.

How to simplify radicals expressions with the same indices?

If two or more radical expressions have the same indices in their denominators, then they are equal to 0 when evaluated at the given values. Thus, to simplify the radicals, you can divide the radical expressions by their common denominator. The result is an equivalent radical expression with a denominator of 1.

How to simplify radical expressions with the same indices?

Let’s say we have the following radical expressions: $$\frac{a}{b}-\frac{c}{b}$$ and $$\frac{a}{b}-c.$$ If you multiply these radical expressions, you get $$a-bc,$$ which is the same as $\frac{a}{b}$. The problem is that you have two different radical signs, so you must simplify one of them first. If you take the radical of the simpler radical expression

How to multiply the radical expressions with the same indices?

There are several ways to multiply radical expressions with the same indices. The two easiest methods are multiplying the radicals and adding the square roots of their denominators.

How to multiply radical expressions with the same indices?

If you have two radical expressions with the same indices, their product is equal to the product of the two original radical expressions (provided that the radical signs match, of course). For example, and are equal to and is equal to