I am working on a problem where a student needs to simplify various radicals. I would like a student to be given sqrt(-48) and they would need to enter 4sqrt(3)i only, and not sqrt(48)i.

I may be overthinking this but I am attempting to use both LimitedRadical Context and Complex Context and I cannot seem to get it right. Here is the current code. Any ideas?

DOCUMENT();

loadMacros(

"PGstandard.pl",

"MathObjects.pl",

"PGML.pl",

"contextFraction.pl",

"contextLimitedRadical.pl",

"PGcourse.pl",

"parserRoot.pl",

"contextLimitedComplex.pl"

);

######################################

Context("Numeric");

$a1 = random(2,7,1);

$a2 = random(2,7,1);

$a3 = random(2,7,1);

$nsqa1 = -$a1*$a1;

$nsqa2 = -$a2*$a2;

$m2 = list_random(2,3);

$b = $nsqa2*$m2;

$nsqa3 = -$a3*$a3;

$m3 = list_random(4,5);

$c = $nsqa3*$m3;

Context("LimitedRadical");

$rad2 = Formula("$a2*sqrt($m2)");

$rad3 = Formula("$a3*sqrt($m3)");

Context("Complex");

$ans2 = Complex("$rad2 i");

$ans3 = Complex("$rad3 i");

Context("LimitedComplex-strict");

$ans1 = Complex("$a1 i");

BEGIN_PGML

Simplify the following expressions.

a. [`\sqrt{[$nsqa1]} = `][_______________]{$ans1}

b. [`\sqrt{[$b]} = `][_______________]{$ans2}

c. [`\sqrt{[$c]} = `][_______________]{$ans3}

END_PGML