Why is it important to simplify radical expressions before adding or subtracting?

In order to to add or subtract radicals together, they must be like radicals; in other words, they must have the EXACT same radicand and index. This is the main reason why we must simplify them.

If you are asked to add or subtract radicals that have different radicands, don't panic. Try to simplify the radicals-->that usually does the trick.

Remember:

Only LIKE radicals can be added or subtracted from one another.

It is important to simplify radical expressions before adding or subtracting because it makes the process easier and reduces the chances of making mistakes. Simplifying radicals involves finding perfect square factors of the radicand, reducing it to its simplest form. By simplifying radicals, you can extract any perfect square factor from under the radical sign, which simplifies calculations and helps to avoid errors. Adding or subtracting simplified radicals allows for a more straightforward and accurate math operation. To simplify radical expressions, follow these steps:

1. Identify the radicand, which is the number or expression inside the radical symbol (√).
2. Find the prime factorization of the radicand. Break it down into its prime factors.
3. Look for pairs of the same prime factors that can be pulled out from under the square root.
4. Rewrite the radical expression by taking out the pairs of the same prime factors.
5. Combine the pulled-out factors outside the radical sign.
6. If there are any remaining factors under the square root, leave them as they are.
7. If any additional simplification is possible, continue simplifying until no further simplification is possible.

After simplifying the radicals, you can then proceed to add or subtract them, ensuring accuracy and efficiency in your calculations.