in reply to Converting a Number into a Radical

I gather we're concerned only with square roots of integers and that, for example, if the answer is sqrt(18), you want to see it presented as 3 x sqrt(2) instead of simply sqrt(18).
To achieve this you'll first want to factorise the integer - you could use something like Math::Factor::XS or Math::Prime::Util.

To stick with the above example, 18 factorises to the primes 2,3,3 - multiply those primes together and you end up with 18.
Notice that the "3" occurs twice - hence you can write the solution as 3 * sqrt(2).
For sqrt(1050) - the prime factors are 2,3,5,5,7, with the "5" occurring twice, and the solution is therefore: 
5 * sqrt(2 * 3 * 7) = 5 * sqrt(42)

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That's essentially how it's done - I don't know if there's a module that does it all for you, or whether you'll have to program a good portion of it yourself. (Perhaps Math::NumSeq might also have something to offer.)

Cheers,
Rob

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Re^2: Converting a Number into a Radical
by slinky773 (Sexton) on Dec 18, 2013 at 08:26 UTC
    Thanks, Rob. That actually really helps.
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Re^2: Converting a Number into a Radical
by hdb (Monsignor) on Dec 20, 2013 at 10:25 UTC

    I could not resist to write it out: 

    use strict;
use warnings;
use Math::Factor::XS 'prime_factors';

my $n = shift;
( $n and $n > 0 and $n == int $n ) or die "Need positive integer as in
+put!\n";

my %p;
$p{$_}++ for prime_factors( $n );

my $radical = 1;
$radical *= $_ for grep { $p{$_}%2 } keys %p;
print "sqrt( $n ) = ", sqrt( $n/$radical ), " * sqrt( $radical )\n";

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    What I was missing is a product function, like sum from List::Util. There is one in the replacement List::Util that comes with Scalar::Util but that means overwriting the standard module which makes me feel uncomfortable.

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Re^2: Converting a Number into a Radical
by Bloodnok (Vicar) on Dec 19, 2013 at 13:49 UTC
    Awesome, syphilis - I wish it were possible to vote it up by more than than one.

    A user level that continues to overstate my experience :-))
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