Dear Sam,

your problem is somewhat insolvable, since the square root of 5 has

an infinite number of digits, so it cannot be represented correctly

on any computer (in decimal or binary notation).

For arbitrary precision calculations with Fixnum exponents, there’s

bigdecimal.

require “bigdecimal”

def calc(n,prec)

# prec is the precision of the sqrt calculations

res=(BigDecimal.new(“2”) ** n)*BigDecimal(“5”).sqrt(prec)

end

puts calc(10000) => 0.44610[several lines of digits]*10^3011 (for

prec=10)

However, don’t believe in too many of these digits…

If you still want to multiply by square roots accurately, it might be a

good

idea to look at continued fractions - every square root has a continued

fraction representation that eventually ends in a periodic pattern.

There is an introduction to arithmetic with them at

*http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html*

(http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html)

Hope that helps,

Axel