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Question 559515: add or subtract the square root of 108x - the square root of 27x
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sqrt(108x - sqrt(27x) equals:
sqrt(36*3x) - sqrt(9*3x) equals:
6*sqrt(3x) - 3*sqrt(3x) equals:
(6-3)*sqrt(3x) equals:
3*sqrt(3x)
confirm by assigning a value to x and solve in the original equation and in the final equation to see that both equations give you the same answer.
use your calculator.
for example:
let x = 32 (random number picked out of the air).
when x = 32, the original equation becomes:
sqrt(108*32) - sqrt(27*32) which becomes:
sqrt(3456) - sqrt(864) which becomes:
29.39387691
when x = 32, the final equation becomes:
3*sqrt(3*32) which becomes:
3*sqrt(96) which becomes:
3*9.797958971 which becomes:
29.39387691
the original equation and the final equation both get the same answer so it looks like the simplification went well.
the simplified expression is:
3*sqrt(3x)
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