How do you simplify sqrt (12) - sqrt (27)?

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Answer 1 · 2018-03-08T19:56:12

See a solution process below:

First, rewrite the expressions in the radicals as:

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

Next, use this rule for radicals to simplify each of the radicals:

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

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

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

#2sqrt(color(blue)(3)) - 3sqrt(color(blue)(3))#

Now, filter out the common term to complete the simplification:

#(2 - 3)sqrt(color(blue)(3)) =>#

#-1sqrt(color(blue)(3)) =>#

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