Factoring numbers with square root terms

Quite often, when doing calculations on polyhedra, you will find yourself with complex equations like \(\frac{20+7\sqrt3}{1+2\sqrt3}\).

Is the top evenly divisible by the bottom? I certainly can’t tell just by looking at them.

There must be a method to factor the numerator.



Lately, I have been doing a lot of math involving square roots of numbers added to square roots, in the form of \(\sqrt{A+B\sqrt{C}}\), this is called a “nested radical.” Normally, you would not be able to simplify any further, unless there was a common factor …Read the Rest