Hello mark090480 Originally Posted by

**mark090480** Hi,

Let's say I have the number 1.414213562, now I know that can be expressed as sqr[2]. If I didn't know that, how could I find it out? I just ask as sometimes I get a number and don't know if there is a better/ more accurate way to express it.

Thanks,

-Mark.

I don't think there's an easy answer to this question.

If you suspect a number is a simple square/cube root, you can simply square/cube it and see what happens. You need to remember, of course, that $\displaystyle 1.414213562$ is only an approximation to $\displaystyle \sqrt2$, so squaring it won't give you an exact answer.

If it's a recurring decimal - like $\displaystyle 0.846153846153...$ - there's a straightforward way to find its corresponding exact fraction. Using that as an example: Let $\displaystyle x = 0.846153846153...$

$\displaystyle \Rightarrow 1000000x = 846153.846153...$

$\displaystyle \Rightarrow 999999x = 846153$ (by subtracting the first equation from the second)

$\displaystyle \Rightarrow x = \frac{846153}{999999}$

You've then got to experiment with cancelling the fraction to reduce it to its simplest terms. This one is:$\displaystyle \frac{11}{13}$

Sometimes, you might just recognise the number; for example $\displaystyle 2.718...$ you may know as the approximate value of $\displaystyle e$; and, of course, $\displaystyle 3.142$ which is approximately $\displaystyle \pi$.

But if the decimal number you've been given is more complicated than this - for example $\displaystyle 0.31783724519578224472575761729617$ - then I think there are no set methods for discovering what it is. (Incidentally, that one is approximately $\displaystyle \sqrt3-\sqrt2$, but I only know that because that's what I started with!)

Grandad