## anonymous 5 years ago what is the square root of 20x over X^3

1. anonymous

$\sqrt{(\frac{20x}{x^3})}$ This?

2. anonymous

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3. anonymous

Well, work with the inside of the square root first. How can you simplify $$\frac{20x}{x^3}$$

4. anonymous

you square out the 20 and get 2 square root 5

5. anonymous

or $2\sqrt{5}$

6. anonymous

I said to ignore the square root first. Just deal with inside the square root for a second.

7. anonymous

$\frac{20x}{x^3}$ Can be simplified to what?

8. anonymous

you would multiply the numerator by $\times ^{3}$ and get $20x ^{4}$

9. anonymous

No. $\frac{20x}{x^3} = \frac{20*x}{x*x*x}$ We can cancel one x from top and bottom. $=\frac{20}{x^2}$

10. anonymous

ohhhh and then I would get $\sqrt{20} \over \sqrt{x ^{?}}$

11. anonymous

Yep

12. anonymous

then get $2\sqrt{5} \over x ^{2}$

13. anonymous

wait

14. anonymous

its $2\sqrt{5} \over \sqrt{x ^{2}}$

15. anonymous

then get $2x ^{2} \sqrt{5}$

16. anonymous

please tell me if that is right!

17. anonymous

No. $$\sqrt{x^2} = |x|$$

18. anonymous

So you have $\frac{2\sqrt{5}}{\sqrt{x^2}} = \frac{2\sqrt{5}}{|x|}$

19. anonymous

I think you should review fractions because you keep moving the things in the denominator up to the numerator.

20. anonymous

You can't really do that.

21. anonymous

$a*b \ne \frac{a}{b}$ Unless a=1 and b=1

22. anonymous

my teacher taught us that way. She said that youcan not have a square root in the demoninator

23. anonymous

No, you can. Often people prefer to have only square roots in the numerator, but in that case you must multiply the top and bottom by an extra factor of the square root. $\frac{a}{\sqrt{b}}$ $= \frac{a}{\sqrt{b}} *1$ $= \frac{a}{\sqrt{b}} *\frac{\sqrt{b}}{\sqrt{b}}$ $= \frac{a\sqrt{b}}{\sqrt{b^2}}$ $= \frac{a\sqrt{b}}{b}$

24. anonymous

yea that looks like the way she said it

25. anonymous

Does that make sense? You cannot just move the square root in the denominator up to the numerator. Otherwise you get bad values. $\frac{a}{\sqrt{b}} = a\sqrt{b} \implies \frac{1}{\sqrt{b}} = \sqrt{b} \implies 1 = \sqrt{b^2} \implies b = 1$ So the only thing you can bring directly from the numerator to the denominator is a 1.

26. anonymous

Or the denominator to the numerator.

27. anonymous

ok

28. anonymous

Are youa teacher?

29. anonymous

I'm not a teacher.. Just a person who's done a lot of math and tutor people. Review your simplification rules for fractions: http://www.khanacademy.org/video/simplifying-rational-expressions-1?playlist=Algebra%20I%20Worked%20Examples

30. anonymous

THANK YOU GOD BLESS YOU!!!! GOODNIGHT