square root of 2m divided by m/s^2?

Answer 1

any number divided by a fraction is the same as multiplying that number by the reciprocal of the bottom number.
The top number is the numerator, the bottom is the denominator. So multiply the numerator by the reciprocal of the denominator. and you get 2 s^2 , the m cancels out

Answer 2

I must PRESUME that your desired result is:

(sqrt 2) s, that is ~ 1.4142... seconds.

Please note that what you were asking would be clearer with the appropriate use of parentheses: (...), square brackets: [...], "curly brackets": {...}, etc.

That way, either in words or in symbols, I believe that your question would have been:

square root of (2m divided by [m/s^2])?, or :

sqrt (2 m / [m/s^2])?

It was with THAT interpretation that I obtained:

(sqrt 2) s, that is ~ 1.4142... seconds.

(The " m's " cancelled out, while the s^2 comes up into the numerator and then gets square-rooted, finally producing the " s .")

WITHOUT indication of such "delimiters," the question you asked could easily have been (mis?)interpreted as:

[sqrt (2m)] / [m/s^2] = {sqrt (2) / [m^(1/2)]} s^2, i.e. sqrt (2) m^(-1/2) s^2.

My first interpretation "smells better," because it LOOKS like the answer to a scientific calculation, with an expected answer in seconds. The second, alternative interpretation (quite possible due to the lack of delimiters) just looks screwy in the end because "m^(-1/2) s^2" looks like NO collection of dimensions that I'VE ever seen.

But really, the onus on making a question clear should not be put on the shoulders of the intended responder(s). YOU should be doing your best to express yourself clearly.

[ LATER EDIT : The answers immediately BEFORE and AFTER mine BEAUTIFULLY illustrate how confused people can be by a string of mathematics or text lacking clarifying delimiters. I could not have asked for better CONFIRMATION of the point I was making ! There is a MORAL here. ]

Live long and prosper.

Answer 3

are there parentheses around the m/s or not? it affects the answer

Answer 4

sqr[2m]/m/s^2 = sqr[2m]s^2/m = sqr[2](s^2)(m^.5)[m^(-1)]
= sqr[2](s^2)m^(-1/2) = sqr[2](s^2)/sqr[m]