Question

How do you combine `\frac { w } { 5} root3(-64) + root3{ 512w ^ { 3 } } / { 5} - \frac { 2} { 5} \sqrt { 50w } - 4\sqrt { 2w }` into a single term, if possible?

Answer 1

`w/5root(3)(-64)+root(3)(512w^3)/5-2/5sqrt(50w)-4sqrt(2w)=(4w)/5-6sqrt(2w)`

Explanation:

`w/5root(3)(-64)+root(3)(512w^3)/5-2/5sqrt(50w)-4sqrt(2w)`

= `w/5root(3)((-4)xx(-4)xx(-4))+root(3)(8wxx8wxx8w)/5-2/5sqrt(5xx5xx2w)-4sqrt(2w)`

= `w/5xx(-4)+(8w)/5-2/5xx5xxsqrt(2w)-4sqrt(2w)`

= `-(4w)/5+(8w)/5-2/cancel5xxcancel5xxsqrt(2w)-4sqrt(2w)`

= `(4w)/5-6sqrt(2w)`