I can't it seems to be ~ to find this prize via google no issue where ns go. I'm make the efforts to resolve a math trouble of rationalizing the molecule in mine pre-calc class and I come upon this and fully forget what happens as soon as you multiply a source by its inverse. Carry out the root and square release out and also it end up being x? go the 2 cancel out and it come to be x * sqrt(x)? go it just stay x2 * sqrt(x)? Any help would it is in appreciated. Thanks.
You are watching: 2x times square root of x
sqrt(x) = x1/2
Therefore:
x2 sqrt(x) = x2 x1/2
By the regulations of exponents this is equal to:
x2+1/2 = x5/2
Which is same to:
sqrt(x5)
Ah, give thanks to you for placing it in that format. Helped me the end a lot. Sometimes I forget straightforward things and it renders things look at a lot more complicated and transforming sqrt right into 1/2 was much easier to check out it together ;P.
I'm not certain why the comment by /u/skaldskaparmal gained downvoted for this reason much.
If it's not immediately obvious to you exactly how to simplify x2 * sqrt(x), then ns think plugging in worths is a good idea.
Of course plugging in worths doesn't prove anything, but it have the right to serve as a good sanity check, and also can quickly eliminate part wrong guesses.
For example, if x is 100, then sqrt(x) is 10. This helps to check whether several of your guesses space plausible, and also it additionally may do it less complicated to visualize why x2 * sqrt(x) simplifies the way it does.
You recognize x2 method x times x. Then x2 * sqrt(x) is x time x times something else. Specifically, if x is 100, then x2 * sqrt(x) is 100 times 100 time 10.
That's a lot bigger 보다 x, i beg your pardon would just be 100. It's additionally bigger than x * sqrt(x), which would be 100 time 10.
Plugging in particular numbers may help you "see" a bit an ext concretely why it's incorrect to "cancel" things in the means that you mentioned.
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True. I did carry out that not quickly after i posted by plugging into my calculator 22 * sqrt(2) and got 4 * sqrt(2) together my answer. Although the took significant off one possible solution I thought of, i still couldn't number it out. I appreciate the solution though!
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