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Simplify the expression.
x times the square root of the quantity 8 x cubed, plus x times the square root of 2, plus four times the square root of the quantity 2x

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- anonymous

\[x \sqrt{8x ^{3}} + x \sqrt{2} + 4\sqrt{2x}\]

- anonymous

I'm usually good at math but this question is a little confusing....
So far I think the answer is 2 because yo can simplify it to get 2x^2sqrt(2x)... and so on

- anonymous

\[2\sqrt{2} \times x \times x ^{3/2} + x \times \sqrt{2} + 4 \sqrt{2} \times x^{1/2} \]

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## More answers

- anonymous

To write it into its raw exponential form.

- anonymous

why did you put fractions in the radical?

- anonymous

By putting the exponents in their fraction forms, you can clearly see their combined values.

- anonymous

This will allow you to factor out an exponential of x, through subtraction of the exponent.

- anonymous

As you can see in this question, the lowest "factorable" term is \[\sqrt{x}\]

- anonymous

I'm only in ninth grade, I don't think this is necessary.. besides, I haven't learned this yet.

- anonymous

I'm not looking for the lowest factorable term.... I'm looking for the leading coefficient when it's in simplified form

- anonymous

But it's factored form looks something like this: \[\sqrt{2} \sqrt{x} (4+\sqrt{x}+2 x^2)\]

- anonymous

To do that, you need write out the terms in full and subtract the exponents when factoring.

- anonymous

I think we're looking for the simplified form not the factored form... \[2x^2 \sqrt{2x} + x \sqrt{2} + 4 \sqrt{2x}\]

- anonymous

Is this fully simplified?

- anonymous

Well, I suppose you can't go any further to "simplify" it without factoring.

- anonymous

ok, so we agree that the leading coefficient is 2?

- anonymous

Okay, thanks, I got it right!

- anonymous

The leading coefficient of the entire term is not 2, its \[2\sqrt{2}\]

- anonymous

100% on my quiz! woot!

- anonymous

Great to hear!

- anonymous

Well, I guess it was the answer they were looking for!

- anonymous

As promised... medal and fan....

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