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How do you simplify #3sqrt(96k)+2sqrt180#?

How do you simplify #3sqrt(96k)+2sqrt180#?
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See a solution process below:

Explanation:

First rewrite each term as:

#3sqrt(16 * 6k) + 2sqrt(36 * 5)#

Next, use this rule for radicals to rewrite each radical:

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

#3sqrt(color(red)(16) * color(blue)(6k)) + 2sqrt(color(red)(36) * color(blue)(5)) =>#

#3sqrt(color(red)(16) * color(blue)(6k)) + 2sqrt(color(red)(36) * color(blue)(5)) =>#

#3sqrt(color(red)(16))sqrt(color(blue)(6k)) + 2sqrt(color(red)(36))sqrt(color(blue)(5)) =>#

#(3 * 4)sqrt(color(blue)(6k)) + (2 * 6)sqrt(color(blue)(5)) =>#

#12sqrt(6k) + 12sqrt(5)#

Now, facture out the common term:

#color(red)(12)sqrt(6k) + color(red)(12)sqrt(5) =>#

#color(red)(12)(sqrt(6k) + sqrt(5))#

answered by: smendyka
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