simplify:

3sqrt(2)+5sqrt(4)+8sqrt(2)-2sqrt(6)

3sqrt(2) + 5sqrt(4) + 8sqrt(2) - 2sqrt(6)

11sqrt(2) + 5*2 - 2sqrt(6)
10 + 11sqrt(2) - 2sqrt(6)

hope this helps~ :)

To simplify the given expression, we can combine the like terms.

First, let's solve for each radical term separately:

- sqrt(2) is already simplified, so we leave it as is.
- sqrt(4) is equal to 2 because the square root of 4 is 2.
- sqrt(6) cannot be simplified further, so we leave it as sqrt(6).

Now, let's simplify the expression:

3sqrt(2) + 5sqrt(4) + 8sqrt(2) - 2sqrt(6)

= 3(sqrt(2)) + 5(2) + 8(sqrt(2)) - 2(sqrt(6))
(distributing the coefficients to the terms inside the parentheses)

= 3sqrt(2) + 10 + 8sqrt(2) - 2sqrt(6)
(multiplying the coefficients with their respective radicals)

Next, let's combine like terms:

= 3sqrt(2) + 8sqrt(2) - 2sqrt(6) + 10
(rearranging the terms)

= (3sqrt(2) + 8sqrt(2)) - 2sqrt(6) + 10
(grouping the like terms together)

= 11sqrt(2) - 2sqrt(6) + 10
(combining the coefficients of the like terms)

Therefore, the simplified expression is 11sqrt(2) - 2sqrt(6) + 10.