## anonymous one year ago Medal + fan 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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1. anonymous

$x \sqrt{8x ^{3}} + x \sqrt{2} + 4\sqrt{2x}$

2. 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

3. anonymous

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

4. anonymous

To write it into its raw exponential form.

5. anonymous

why did you put fractions in the radical?

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

Is this fully simplified?

15. anonymous

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

16. anonymous

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

17. anonymous

Okay, thanks, I got it right!

18. anonymous

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

19. anonymous

100% on my quiz! woot!

20. anonymous

Great to hear!

21. anonymous

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

22. anonymous

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