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Question 615796: Nakim simplified 3 times the square root of 2x plus x times the square root of 8x minus 5 times the square root of 18x and got -10x times the square root of 2x for an answer.
Part 1: Using complete sentences, explain what Nakim did wrong.
Part 2: Show all your work to simplify the expression.
i am confused because we didnt learn how to do anything like this in the lesson.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! nakim messed up on the first part of the problem.
this problem has to do with the distributive law of multiplication applied to square roots.
the problem states to simplify the following expression.
3*sqrt(2x)
+ x*sqrt(8x)
- 5*sqrt(18x)
notice that the first term is 3*sqrt(2x).
it is NOT 3x*sqrt(2x)
the solution to the problem converts everything under the square root sign to sqrt(2x) in the following manner.
3*sqrt(2x) = 3*sqrt(2x)
this remains the same.
x*sqrt(8x) = x*sqrt(4*2x) = x*sqrt(4)*sqrt(2x) = 2x*sqrt(2x)
the 8x under the square root sign was factored to get 4*2x which allowed you to take the perfect square of 4 out of the square root sign and make it equal to 2.
5*sqrt(18x) = 5*sqrt(9*2x) = 5*sqrt(9)*sqrt(2x) = 5*3*sqrt(2x) = 15*sqrt(2x)
the 18x under the square root sign was factored to get 9*2x which allowed you to take the perfect square of 9 out of the square root sign and make it equal to 3.
you were left with:
3*sqrt(2x)
+ 2x*sqrt(2x)
- 15x*sqrt(2x)
this is where nakim went wrong.
he assumed that 3*sqrt(2x) was equal to 3x*sqrt(2x)
that allowed him to combine all results to get:
3x*sqrt(2x) + 2x*sqrt(23x) - 15*sqrt(2x) is equal to:
(3x+2x-15x)*sqrt(2x) which then became equal to:
-10x*sqrt(2x)
that's the only way that nakim could get the answer that he got.
unfortunately, the first term is not 3x*sqrt(2x), but is 3*sqrt(2x) which means that it couldn't be combined because they're not common terms. 3x is not the same as 3.
you can add 3x and 2x to get 5x, but you can't add 3 + 2x to get 5x. they can't be combined because the variables are different.
the correct answer would be:
3*sqrt(2x) + 2x*sqrt(2x) - 15x*sqrt(2x) which can be combined into:
(3 + 2x - 15x)*sqrt(2x) which can be further combined into:
(3 - 13x)*sqrt(2x)
this can either be left as is or simplified further into:
3*sqrt(2x) - 13x*sqrt(2x) depending on what your instructor expects to see.
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