Question

Simplify as much as possible.

Assume that all variables represent positive real number
4x

√32xv^2 + v√2x^3

Answer 1

`4x √(32xv^2)+v √(2x^3) = 4x √(16.2) . √(x) . √(v^2) + v √(2) . √(x^2) . x`

`= 4x . √(2) . √(x) . v + v √(2) . x √(x) = 16 xv √(2x) + xv √(2x)` =
`17√(2x)`

Answer 2

`4x√(32xv^2)+v√(2x^3)=4x√(16\cdot2)\cdot√(x)\cdot√(v^2)+v\sqrt2\cdot√(x^2\cdot x)\\\\=4x\cdot4\sqrt2\cdot√(x)\cdot v+v\sqrt2\cdot x√(x)=16xv√(2x)+xv√(2x)=17√(2x)\\\\========================================\\\\D;\\x\in < 0;\ \infty)\ \wedge\ v\in\mathbb{R}`