I would not leave a radical in the denominator. Most math teachers will request that you rationalize denominators.
It's a simple process. 6/√29 = 6×√29 / (√29/√29) = 6√29 / 29.
Note that the radical is no longer in the denominator. And we did this by multiplying by 1, so the value of the number has not changed, only its appearance. √29 / √29 = 1.
Similarly, 15 / √29 should be rationalized as 15√29/29.
James S.
tutor
It is not an arbitrary rule at all. It has some of the same benefits as reducing fractions. It establishes a unique format for numbers that have radical and non-radical parts, similar to the unique format of a fully reduced fraction. Math teachers expect this format for this type of number, just like they expect fractions to be simplified.
Report
09/18/23
William C.
I see your point. We do the same type of thing in always expressing complex numbers as a +bi and never leave an imaginary term in the denominator. And Imaginary terms are pretty much just radical terms in disguise since i = √(-1).
Report
09/18/23
William C.
I have never been a fan of unnecessary rules that make an answer arbitrarily more cumbersome. This might be a reason I chose not to be a math major in college (even though I loved math). ;-)09/18/23