How do you simplify #3sqrt24-sqrt54+sqrt6#?

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Answer 1 · 2017-08-02T21:18:41

See a solution process below:

First, rewrite the expression as:

#3sqrt(4 * 6) - sqrt(9 * 6) + sqrt(6)#

Use this rule for radicals to simplify the individual terms:

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

#3sqrt(color(red)(4) * color(blue)(6)) - sqrt(color(red)(9) * color(blue)(6)) + sqrt(6) =>#

#3sqrt(color(red)(4))sqrt(color(blue)(6)) - sqrt(color(red)(9))sqrt(color(blue)(6)) + sqrt(6) =>#

#6sqrt(6) - 3sqrt(6) + sqrt(6)#

We can now factor out the common factor in each term and combine the remainders:

#6sqrt(6) - 3sqrt(6) + 1sqrt(6) =>#

#(6 - 3 + 1)sqrt(6) =>#

#4sqrt(6)#