SOLUTION: Perform the indicated operations: 2√[48] + 7√[12] –√[27] I have no clue how to even start this one..

Algebra ->  Radicals -> SOLUTION: Perform the indicated operations: 2√[48] + 7√[12] –√[27] I have no clue how to even start this one..      Log On


   

Question 144232: Perform the indicated operations:
2√[48] + 7√[12] –√[27]
I have no clue how to even start this one..
Found 3 solutions by scott8148, Earlsdon, stanbon:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
factoring __ 2(sqrt(16))(sqrt(3))+7(sqrt(4))(sqrt(3))-(sqrt(9))(sqrt(3))

2(4)(sqrt(3))+7(2)(sqrt(3))-(3)(sqrt(3)) __ 8(sqrt(3))+14(sqrt(3))-3(sqrt(3)) __ 19(sqrt(3))

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Think perfect squares!
Evaluate:
2sqrt%2848%29%2B7sqrt%2812%29-sqrt%2827%29 Now factor each radicand (the number under the radical sign) so that one of the factors in each is a perfect square.
2sqrt%2816%2A3%29%2B7sqrt%284%2A3%29-sqt%289%2A3%29 Now rewrite this to show the squared numbers.
2sqrt%284%5E2%2A3%29%2B7sqrt%282%5E2%2A3%29-sqrt%283%5E2%2A3%29 Now take the square root of the squared numbers and move them outside of the radical.
2%2A4sqrt%283%29%2B7%2A2sqrt%283%29-3sqrt%283%29 Simplify this a bit.
8sqrt%283%29%2B14sqrt%283%29-3sqrt%283%29 Now factor out the sqrt%283%29.
%288%2B14-3%29sqrt%283%29 Simplify.
19sqrt%283%29...and there it is!

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2√[48] + 7√[12] –√[27]
------------------------
You need to find the highest perfect square factor in 48,12,27.
--------------------------
= 2sqrt(16*3) + 7sqrt(4*3) - sqrt(9*3)
Take the square root of the perfect square factors out of the radical to get:
----------------------------
= 2*4sqrt(3) + 7*2sqrt(3) - 3sqrt(3)
= 8sqrt(3) + 14sqrt(3) - 3sqrt(3)
Simplify to get:
= 19sqrt(3)
=====================
Cheers,
Stan H.