what is the square root of 20x over X^3

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what is the square root of 20x over X^3

Mathematics
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\[\sqrt{(\frac{20x}{x^3})}\] This?
YEEEESSSSSSSSSSSSSSSSSSSSSS
Well, work with the inside of the square root first. How can you simplify \(\frac{20x}{x^3}\)

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you square out the 20 and get 2 square root 5
or \[2\sqrt{5}\]
I said to ignore the square root first. Just deal with inside the square root for a second.
\[\frac{20x}{x^3}\] Can be simplified to what?
you would multiply the numerator by \[ \times ^{3}\] and get \[20x ^{4}\]
No. \[\frac{20x}{x^3} = \frac{20*x}{x*x*x}\] We can cancel one x from top and bottom. \[=\frac{20}{x^2}\]
ohhhh and then I would get \[\sqrt{20} \over \sqrt{x ^{?}}\]
Yep
then get \[2\sqrt{5} \over x ^{2}\]
wait
its \[2\sqrt{5} \over \sqrt{x ^{2}}\]
then get \[2x ^{2} \sqrt{5} \]
please tell me if that is right!
No. \(\sqrt{x^2} = |x|\)
So you have \[\frac{2\sqrt{5}}{\sqrt{x^2}} = \frac{2\sqrt{5}}{|x|} \]
I think you should review fractions because you keep moving the things in the denominator up to the numerator.
You can't really do that.
\[a*b \ne \frac{a}{b} \] Unless a=1 and b=1
my teacher taught us that way. She said that youcan not have a square root in the demoninator
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. \[\frac{a}{\sqrt{b}} \] \[= \frac{a}{\sqrt{b}} *1 \] \[= \frac{a}{\sqrt{b}} *\frac{\sqrt{b}}{\sqrt{b}} \] \[= \frac{a\sqrt{b}}{\sqrt{b^2}} \] \[= \frac{a\sqrt{b}}{b}\]
yea that looks like the way she said it
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.
Or the denominator to the numerator.
ok
Are youa teacher?
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
THANK YOU GOD BLESS YOU!!!! GOODNIGHT

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