Question

Why are radicals simplified before adding and subtracting? Explain your reasoning by adding the square root of 8 and the square root of 32.

Answer 1

The reason they have to be simplified is that you cannot add radical unless the number under the radical is the same on all of them.

For example:

If you add √8 + √32 without simplifying, the best you could do is an estimate. But if you're required to put your answer in standard radical form this would be an issue.

So, you would have to simplify to combine:

√4√2 + √16√2
2√2 + 4√2
6√2

Hope this helped!