Radical question

[Holocene]

With regard to examinations, is it true that radicals must typically be "reduced", if possible?

For instance, with fractions, you would hardly ever leave 4/8 as it is, but instead reduce it to 1/2.

Well let's say that durring an exam, you arrived at \displaystyle{\sqrt[3]{81}} for an answer.

Is it true that normal procedure is to instead express that as \displaystyle{3\sqrt[3]{3}} ???

Thanks a lot.

[jcsd]

Yes is the answer. It's just good practice.

Though in the example you've cited expressing the answer as 3^{\frac{4}{3}} doesn't seem wrong to me.

[Invictious]

Yes, expressing it still in surd form or in power form is generally fine, unless they specifically ask you do express it in some other form.

Though if it is the final step of a question, I would leave it as surd form, simplified, rather than leaving it in a power form, unless there are more calculations to follow, which require indices etc.