PLS HELP ME
Simplify. All variables represent non-negative real numbers.
*problem attached

Question

PLS HELP ME
Simplify. All variables represent non-negative real numbers.
*problem attached

anonymous · Answer

$$c \sqrt{75c} - \sqrt{27c ^{3}}$$

anonymous · Answer

please explain all the steps

whpalmer4 · Answer

Well, when faced with a radical sign, try to factor what's underneath.  For example, $75 = 5*5*3$, so $\sqrt{75} = \sqrt{5*5*3} = \sqrt{5*5}*\sqrt{3} = 5\sqrt{3}$.

whpalmer4 · Answer

You can similarly factor 27 and c^3.

whpalmer4 · Answer

Try it, report your answer, and I'll check your work.

anonymous · Answer

I honestly don't get it.

whpalmer4 · Answer

What are the factors of 27?  What are the factors of c^3?

anonymous · Answer

there's 9 and 3?

anonymous · Answer

and c^2?

whpalmer4 · Answer

Yes, so you can write $27$ as $9*3$, and $c^3$ as $c^2*c$.  How would you simplify those if they were under a square root?  Look back at the 75 example.

anonymous · Answer

$$\sqrt{9} * \sqrt{c^2} * \sqrt{3c}$$

anonymous · Answer

which would simplify to $$3c \sqrt{3c}$$

whpalmer4 · Answer

Very good!  Now finish up the work on the first term, and combine them for the full answer.