Question

I need help completing this problem ASAP

Answer 1

D.
`3x√(2x)`

Explanation:

The problem gives on the following equation:

`√(32x^3)+-√(16x^3)+4√(x^3)-2√(x^3)`

Alongside the information that (
`x\geq0`).

One must bear in mind that the operation (
`\sqrt`) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,

`√(2*2*2*2*2*x*x*x)-√(2*2*2*2*x*x*x)+4√(x*x*x)-√(2*x*x*x)`

Now remove the duplicate factors from underneath the radical,

`2*2*x√(2x)-2*2*x√(x)+4x√(x)-2x√(x)`

Simplify,

`4x√(2x)-4x√(x)+4x√(x)-x√(2x)`

`3x√(2x)`