SOLUTION: Simplest form of radical expression. Please explain 3 square root 24 - 2 square root 54 + 2 square root 18

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Question 685776: Simplest form of radical expression. Please explain
3 square root 24 - 2 square root 54 + 2 square root 18
Found 3 solutions by stanbon, funmath, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3 square root 24 - 2 square root 54 + 2 square root 18
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3 sqrt(4*6) - 2 sqrt(9*6) + 2 sqrt(9*2)
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= 3*2 sqrt(6) - 2*3 sqrt(6) + 2*3 sqrt(2)
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= (6-6)sqrt(6) + 6 sqrt(2)
----
= 6 sqrt(2)
================
Cheers,
Stan H.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Simplest form of radical expression. Please explain
3 square root 24 - 2 square root 54 + 2 square root 18
3sqrt%2824%29-2sqrt%2854%29%2B2sqrt%2818%29
You can either look for perfect squares, and take the square root of that part...or use any prime factors that you two of.
3sqrt%282%2A2%2A2%2A3%29-2sqrt%282%2A3%2A3%2A3%29%2B2sqrt%282%2A3%2A3%29
3sqrt%284%2A6%29-2sqrt%289%2A6%29%2B2sqrt%289%2A2%29
3sqrt%284%29sqrt%286%29-2sqrt%289%29sqrt%286%29%2B2sqrt%289%29sqrt%282%29
3%282%29sqrt%286%29-2%283%29sqrt%286%29%2B2%283%29sqrt%282%29
6sqrt%286%29-6sqrt%286%29%2B6sqrt%282%29
The only ones you can add and subtract are the like terms. They have to have the same indexes and roots in order to add them.
%286-6%29sqrt%286%29%2B6sqrt%282%29
0%2B6sqrt%282%29
highlight%286sqrt%282%29%29
Hope that was clear...wish I could point and talk to explain. lol

Answer by MathLover1(20849) About Me  (Show Source):