simplify as much as possible.
Assume that all variables represent positive real number
4x√32xv^2 + v√2x^3
√32 = 4√2, so we have
4x*4√2xv^2 + v√2x^3
16x√2x√v^2 + v√2x√x^2
16xv√2x + vx√2x
17vx√2x
To simplify the expression 4x√32xv^2 + v√2x^3, we can simplify each square root term separately and then combine them.
First, let's simplify the first term 4x√32xv^2.
Step 1: Simplify the square root term inside the parentheses.
√32 = √(16 * 2) = (√16) * (√2) = 4√2
Step 2: Rewrite the expression with the simplified square root term.
4x√32xv^2 = 4x * 4√2 * x * v^2 = 16x^2√2v^2
Now, let's simplify the second term v√2x^3.
Step 1: Simplify the square root term inside the parentheses.
√2x^3 = √(2 * x^2 * x) = (√2) * (√x^2) * (√x) = √2 * x * √x = x√2x
Now, let's combine the simplified terms:
16x^2√2v^2 + x√2x = (16x^2v^2 + xv)√2x
Therefore, the simplified expression is (16x^2v^2 + xv)√2x.