What is 13 root 3 - 4 root 48 in radical form?

1 Answer
Jul 18, 2017

Answer:

If the question is to simplify this expression: #13sqrt(3) - 4sqrt(48)#

Then see a solution process below:

Explanation:

First, rewrite the radical on the right as:

#13sqrt(3) - 4sqrt(16 * 3)#

Now, use this rule of radicals to simplify the term on the right:

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

#13sqrt(3) - 4sqrt(color(red)(16) * color(blue)(3)) =>#

#13sqrt(3) - 4sqrt(color(red)(16))sqrt(color(blue)(3)) =>#

#13sqrt(3) - (4 * 4sqrt(color(blue)(3))) =>#

#13sqrt(3) - 16sqrt(color(blue)(3))#

Next, factor our the common term to simplify the constants:

#(13 - 16)sqrt(color(blue)(3)) =>#

#-3sqrt(3)#