How do you simplify #(sqrt75-sqrt27)/sqrt12#?

1 Answer
Mar 19, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite each of the radicals as:

#(sqrt(25 * 3) - sqrt(9 * 3))/sqrt(4 * 3)#

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

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

#(sqrt(color(red)(25) * color(blue)(3)) - sqrt(color(red)(9) * color(blue)(3)))/sqrt(color(red)(4) * color(blue)(3)) =>#

#(sqrt(color(red)(25))sqrt(color(blue)(3)) - sqrt(color(red)(9))sqrt(color(blue)(3)))/(sqrt(color(red)(4))sqrt(color(blue)(3))) =>#

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

Next, factor out the common term in the numerator:

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

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

#1#