SOLUTION: Combine: 3sqrt48-12sqrt75+4sqrt12 also if you could show how you solved I would greatly appreciate it.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Combine: 3sqrt48-12sqrt75+4sqrt12 also if you could show how you solved I would greatly appreciate it.      Log On


   

Question 148466: Combine:
3sqrt48-12sqrt75+4sqrt12
also if you could show how you solved I would greatly appreciate it.
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
3sqrt%2848%29-12sqrt%2875%29%2B4sqrt%2812%29
Fine sqrt%2848%29, sqrt%2875%29, and sqrt%2812%29 first.
Let's start with sqrt%2848%29. Find two factors of 48, one of which is a perfect square. How about 16 and 3?

sqrt%2848%29=sqrt%2816%29sqrt%283%29 or 4sqrt%283%29.

Follow the same procedure for sqrt%2875%29 and sqrt%2812%29. Your answers respectively will be 5sqrt%283%29 and 2sqrt%283%29. Now plug those back into the original equation:

3sqrt%2848%29-12sqrt%2875%29%2B4sqrt%2812%29 becomes
3%284sqrt%283%29%29-12%285sqrt%283%29%29%2B4%282sqrt%283%29%29

Simplify this by multiplying and get
12sqrt%283%29-60sqrt%283%29%2B8sqrt%283%29

Since they all end in sqrt%283%29, just add or subtract as indicated:
12sqrt%283%29-60sqrt%283%29%2B8sqrt%283%29=-40sqrt%283%29

Answer: 3sqrt%2848%29-12sqrt%2875%29%2B4sqrt%2812%29=-40sqrt%283%29