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.
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.