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?

Question

Aurora Arias · Accepted Answer

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

Genesis Amaya · Answer

undefined To combine the given expression into a single term, we can simplify each term individually and then combine like terms.

First, let's simplify each term:

1. $ \frac { w } { 5} \sqrt{3}(-64) $ simplifies to $ -\frac { 64w } { 5} \sqrt{3} $.
2. $ \frac { \sqrt{3} \sqrt[3]{512w^3} } { 5} $ simplifies to $ \frac { \sqrt{3} \cdot 8w \sqrt[3]{w} } { 5} $, which further simplifies to $ \frac { 8w^2\sqrt{3} } { 5} $.
3. $ -\frac { 2} { 5} \sqrt { 50w } $ remains the same.
4. $ -4\sqrt { 2w } $ remains the same.

Now, let's combine like terms:

$$ -\frac { 64w } { 5} \sqrt{3} + \frac { 8w^2\sqrt{3} } { 5} - \frac { 2} { 5} \sqrt { 50w } - 4\sqrt { 2w } $$

$$ = \frac { -64w + 8w^2 } { 5} \sqrt{3} - \frac { 2} { 5} \sqrt { 50w } - 4\sqrt { 2w } $$

Thus, the given expression can be combined into a single term as:

$$ \frac { -64w + 8w^2 } { 5} \sqrt{3} - \frac { 2} { 5} \sqrt { 50w } - 4\sqrt { 2w } $$