Question 187924
You need to factor each of these terms and then factor out any common factor.
Let's take each term, one-by-one, and see how that's done.
{{{sqrt(12x^5)}}} this can be written as:
{{{sqrt(4*3*x^4*x)}}} Notice that 4 and {{{x^4 = (x^2)^2}}} are perfect squares so you can take their square roots and move them outside of the radical sign.
{{{highlight(sqrt(12x^5) = 2x^2sqrt(3x))}}}
Similarly for the second term:
{{{sqrt(300x^5)}}} Factor 300 into {{{300 = 3*10^2}}} and {{{x^5 = x*(x^2)^2}}} and again, you have some perfect squares {{{10^2}}} and {{{(x^2)^2}}} so take their square roots and move them outside of the radical sign.
{{{highlight(sqrt(300x^5) = 10x^2*sqrt(3x))}}}
and for the last term:
{{{2x*sqrt(48x^3)}}} you have {{{48 = 3*16}}}={{{3*4^2}}} and {{{x^3 = x*x^2}}}, so...
{{{2x*sqrt(48x^3) = 2x*4x*sqrt(3x)}}}={{{highlight(8x^2sqrt(3x))}}}
Now let's put it all together:
{{{2x^2*sqrt(3x)+10x^2*sqrt(3x)-8x^2*sqrt(3)}}} Factor the common factor{{{sqrt(3x)}}} to get:
{{{sqrt(3x)(2x^2+10x^2-8x^2)}}} Now add up the {{{x^2}}} terms and you get:
{{{highlight(4x^2*sqrt(3x))}}}