How do you simplify #12sqrt15 - 9sqrt75 + 8sqrt45 - 6sqrt225#?

1 Answer
Jul 9, 2017

Answer:

See a solution process below:

Explanation:

First, we can rewrite the expression as:

#12sqrt(15) - 9sqrt(25 * 3) + 8sqrt(9 * 5) - (6 * 15) =>#

#12sqrt(15) - 9sqrt(25 * 3) + 8sqrt(9 * 5) - 90#

Now we can rewrite the radicals using this rule for radicals:

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

#12sqrt(15) - 9sqrt(color(red)(25) * color(blue)(3)) + 8sqrt(color(red)(9) * color(blue)(5)) - 90 =>#

#12sqrt(15) - 9sqrt(color(red)(25))sqrt(color(blue)(3)) + 8sqrt(color(red)(9))sqrt(color(blue)(5)) - 90 =>#

#12sqrt(15) - (9 * 5)sqrt(color(blue)(3)) + (8 * 3)sqrt(color(blue)(5)) - 90 =>#

#12sqrt(15) - 45sqrt(color(blue)(3)) + 24sqrt(color(blue)(5)) - 90 =>#