How do you simplify #sqrt12-sqrt75#?

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Answer 1 · 2018-03-09T15:05:21

See a solution process below"

First, rewrite the radicals as:

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

Next, use this rule for exponents to rewrite and simplify each radical:

#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)(25) * color(blue)(3)) =>#

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

#2sqrt(color(blue)(3)) - 5sqrt(color(blue)(3))#

Now, factor out the common term:

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

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