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

1 Answer
Mar 8, 2018

Answer:

See a solution process below:

Explanation:

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))#