How do you simplify #2sqrt6+3sqrt54#?
The answer is
Assuming you know how to simplify individual radicals, we can get more into detail about how to do this. With radicals, if they have the same base (as in the same number under the square root sign), we can simply add the coefficients together (The numbers in front of the square root sign).
However, we see that
To do this, we need to find perfect square factors (4, 9, 16) that can be found by breaking down the 54. What it comes out to be is 9 and 6, very nice numbers to work with:
As the 9 is a perfect square of 3, it can be brought out to the front of the equation, forming
Hope this helped to clarify how to solve radicals with different bases!