How do you simplify #4sqrt 27-11sqrt 20-sqrt48+7sqrt45#?

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Answer 1 · 2017-07-15T22:21:00

See a solution process below:

First, rewrite the terms within the radicals as:

#4sqrt(9 * 3) - 11sqrt(4 * 5) - sqrt(16 * 3) + 7sqrt(9 * 5)#

We can now use this rule of radicals to simplify the radicals:

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

#4sqrt(9)sqrt(3) - 11sqrt(4)sqrt(5) - sqrt(16)sqrt(3) + 7sqrt(9)sqrt(5) =>#

#(4 * 3sqrt(3)) - (11 * 2sqrt(5)) - 4sqrt(3) + (7 * 3sqrt(5)) =>#

#12sqrt(3) - 22sqrt(5) - 4sqrt(3) + 21sqrt(5)#

We can now group and combine like terms:

#12sqrt(3) - 4sqrt(3) - 22sqrt(5) + 21sqrt(5) =>#

#(12 - 4)sqrt(3) + (-22 + 21)sqrt(5) =>#

#8sqrt(3) + (-1)sqrt(5) =>#

#8sqrt(3) - sqrt(5)#