Let's simplify this expression step by step:

First, let's simplify inside the square root:

√(16 + 8√5) = √(16) + √(8√5)
√(16) = 4
√(8√5) = √(4*2√5) = 2√(2√5)

So, √(16 + 8√5) becomes:

4 + 2√(2√5)

Now, let's simplify the second expression inside the square root:

√(16 - 8√5) = √(16) - √(8√5)
√(16) = 4
√(8√5) = √(4*2√5) = 2√(2√5)

So, √(16 - 8√5) becomes:

4 - 2√(2√5)

Now, adding these two expressions together:

(4 + 2√(2√5)) + (4 - 2√(2√5))
= 4 + 2√(2√5) + 4 - 2√(2√5)
= 8

Therefore, [3]√(16 + 8√5) + [3]√(16 - 8√5) equals 8.