How do you simplify #4sqrt27-sqrt75#?

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Answer 1 · 2018-03-14T17:59:20

See a solution process below:

First, rewrite the two radicals as:

#4sqrt(9 * 3) - sqrt(25 * 3)#

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

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

#4sqrt(color(red)(9) * color(blue)(3)) - sqrt(color(red)(25) * color(blue)(3)) =>#

#4sqrt(color(red)(9))sqrt(color(blue)(3)) - sqrt(color(red)(25))sqrt(color(blue)(3)) =>#

#(4 * 3sqrt(color(blue)(3))) - 5sqrt(color(blue)(3)) =>#

#12sqrt(color(blue)(3)) - 5sqrt(color(blue)(3))#

Now, combine the like terms:

#(12 - 5)sqrt(color(blue)(3)) =>#

#7sqrt(color(blue)(3))#