How do you simplify # (3 sqrt(x^3)) times (4 + 2 sqrt(xy))#?

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Answer 1 · 2018-01-08T12:24:29

See a solution process below:

First, multiply each term within the right parenthesis by the term on the left:

#(color(red)(3sqrt(x^3))) xx (4 + 2sqrt(xy)) =>#

#(color(red)(3sqrt(x^3)) xx 4) + (color(red)(3sqrt(x^3)) xx 2sqrt(xy)) =>#

#12sqrt(x^3) + 6sqrt(x^3)sqrt(xy)#

Next, we can use this rule to combine the radicals in the term on the right:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#12sqrt(x^3) + 6sqrt(color(red)(x^3))sqrt(color(blue)(xy)) =>#

#12sqrt(x^3) + 6sqrt(color(red)(x^3) * color(blue)(xy)) =>#

#12sqrt(x^3) + 6sqrt(x^4y)#

Then, we can use the opposite of the above rule to reduce the radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#12sqrt(x^3) + 6sqrt(x^4y) =>#

#12sqrt(color(red)(x^2) * color(blue)(x)) + 6sqrt(color(red)(x^4) * color(blue)(y)) =>#

#12sqrt(color(red)(x^2))sqrt(color(blue)(x)) + 6sqrt(color(red)(x^4))sqrt(color(blue)(y)) =>#

#12xsqrt(x) + 6x^2sqrt(y)#