4√5√√48+3√40√√12-2√15√√27

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To simplify this expression, we first need to simplify the square roots within the radical signs.

√48 = √(163) = √16 √3 = 4√3
√40 = √(410) = √4 √10 = 2√10
√15 = 3√5
√27 = 3√3

Now our expression becomes:

4√5 4√3 + 3√5 2√10 - 2√5 * 3√3

Which simplifies to:

16√15 + 6√50 - 6√15

Now, we simplify the radicals under the radical sign:

√50 = √(25*2) = 5√2

So, the expression becomes:

16√15 + 6(5√2) - 6(√15)
16√15 + 30√2 - 6√15
(16 - 6)√15 + 30√2
10√15 + 30√2

Therefore, the simplified expression is 10√15 + 30√2.