How do you combine #-10\sqrt { 20x ^ { 3} } + 7\sqrt { 80x ^ { 3} }#?

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Answer 1 · 2017-11-09T14:03:07

See a solution process below:

First, rewrite the radical terms using this rule for radicals:

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

#-10sqrt(color(red)(4x^2) * color(blue)(5x)) + 7sqrt(color(red)(16x^2) * color(blue)(5x))#

#-10sqrt(color(red)(4x^2))sqrt(color(blue)(5x)) + 7sqrt(color(red)(16x^2))sqrt(color(blue)(5x))#

#(-10 * 2x)sqrt(color(blue)(5x)) + (7 * 4x)sqrt(color(blue)(5x))#

#-20xsqrt(color(blue)(5x)) + 28xsqrt(color(blue)(5x))#

We can now factor out common terms and calculate the result:

#(-20 + 28)xsqrt(color(blue)(5x))#

#8xsqrt(color(blue)(5x))#