Square root of negative numbers If:

$$a = \sqrt{ b^2 - b }$$

The problem I have is that for values of:

$0 &lt; b &lt; 1$ 

the result of:

$b^2 - b$

Is a negative number which gives rise to an error on Excel and my calculator.

I understand that negative numbers don't have square roots (I read it on Wikipedia at least), so how do I solve this for values of $b$ less than 1?

Thanks! :)
Mathematicians have defined a new number, called $i$, such that $i^2=-1$ (it's not really that new). Commonly $i$ is called an imaginary number. If you're familiar with coordinate geometry like the Cartesian plane, the complex numbers are very similar. Every complex number has the form $a+bi$ for some $a,b\in\mathbb{R}$ so we can plot complex numbers (that is, numbers that have a real part and an imaginary part) as pairs (a,b) where we view the typical $x$-axis as the real part and the $y$-axis as the imaginary axis. If you have a number like $\sqrt{-64}$, you can simplify it by pulling out the $-1$ as an $i$. That is,
$$
\sqrt{-64}=i\sqrt{64}=\pm8i
$$
Complex numbers have lots of interesting properties. I recommend checking out the wikipedia page on complex numbers for more information.

Specifically to answer your question, if $b^2-b&lt;0$, there are no solutions over the real numbers. You need to use complex numbers in order to find solutions.
Svenkat's and Google answers:
&quot;one cannot take the square root of negative numbers&quot;
&quot;Negative numbers don't have real square roots&quot;
&quot;you can't take the square root of a negative number&quot;
It is very difficult to break 16th century scholastic dogma, e.g. imaginary numbers, used in taking the square root of negative numbers. Nobody wants to discuss or in other words - taboo.
If we are consistent, we should accept to take square roots only from positive numbers. The result of multiplication of the same numbers is always a positive number.
If we take the square root of a negative number, we should place the negative sign before the radical sign/radix -√. Details: https://globid.eu/