How to Divide Radical Expressions

Dividing radical expressions is similar to multiplying them. We’re going to use this rule that the square root of A, divided by the square of B, is equal to the square root of A divided by B.

Our first example is the square root of 50 divided by the square root of 2. According to our rule, we can rewrite this as the square root of 50 divided by 2. Then, since we can divide 50 by 2, we will to simplify it.

The square root of 50 divided by 2 is the square root of 25. 25 is a perfect square, so we can simplify further by taking the square root of 25, which is 5.

On this next example, we’re going to use this rule in reverse, since we can’t divide 9 by 16. If we use this rule in reverse, I can break it up to write it as the square root of 9 divided by the square root of 16.

9 and 16 are both perfect squares. We take the square root of 9. We get 3. The square root of 16 is 4. Therefore, the square root of 9/16 is 3/4. Let’s look at one more example.

The square root of 48 divided by the square root of 6. On this one, we’re again going to use that rule to write it as one square root division problem, since 48 and 6- neither one of those are perfect squares.

We can’t take the square root of those just yet. We could, but we wouldn’t get a perfect square. The square root of 48 divided by the square root of 6 could be rewritten as the square root of 48 divided by 6. 48 divided by 6 is 8.

That’s the square root of 8. 8 is not a perfect square, but it does have a perfect square factor of 4. We can rewrite this as the square root of 4 times the square root of 2. The square root of 4 is 2, times the square root of 2 would be two square roots of 2. The square root of 48 divided by the square root of 6 would be two square roots of 2.