Simplify the expression. Variables are assumed to have positive values. Show your work/thinking.

Question

5 square root of 8x^3 + 3 square root of 18x^3

Answer 1

First, we can simplify under the square roots separately:

Square root of 8x^3 = Square root of (4 * 2 * x^2 * x) = 2x sqrt(2x)

Square root of 18x^3 = Square root of (9 * 2 * x^2 * x) = 3x sqrt(2x)

Now plug these back into the original expression:

5 * 2x sqrt(2x) + 3 * 3x sqrt(2x)
= 10x sqrt(2x) + 9x sqrt(2x)
= 19x sqrt(2x)

Therefore, the simplified expression is 19x sqrt(2x).