You haven't mentioned whether you want to solve this as a simplified radical or not.
If so:
√20
= √(4 x 5)
=√(2² x 5)
=2 √5
If however you are looking for the exact answer in decimal notation, Newton's method (http://en.wikipedia.org/wiki/Newton's_method) can be used to provide successive iterations:
x = √20
Can be rewritten as the equation:
x² -20 = 0
With a first derivative
f'(x) = 2x
Given that 4² = 16 and 5² = 25, an initial estimate of midway, i.e. 4.5 sounds a reasonable first estimate for x0:
x1 = x0 - f(x0)/f'(x0)
= 4.5 - ((4.5)² - 20) / (2 x 4.5)
= 4.5 - 0.02777...
= 4.47222...
A second iteration would thus be
4.47222... - ((4.47222)² -20) / (2 x 4.47222...)
=4.472136...
Further iteration will yield improved accuracy.
However, if you use a calculator to check your answer, you will see that we are already accurate to 5 decimal places of the true answer 4.472135954999579...