# SimplifiedSquareRoots

## Simplified Square Roots in Student Answers

This PG code shows how to require student answers to be completely reduced square roots.

PG problem file Explanation
DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"contextLimitedPowers.pl"
);

TEXT(beginproblem());


Initialization: We need to include the macros file contextLimitedPowers.pl.

###########################
#
# Subclass the numeric functions
#
package my::Function::numeric;
our @ISA = ('Parser::Function::numeric');

#
# Override sqrt() to return a special value (usually 1) when evaluated
# effectively eliminating it from the product.
#
sub sqrt {
my $self = shift; my$value = $self->context->flag("setSqrt"); return$value+1 if $value &&$_ == 1; # force sqrt(1) to be incorrect
return $value if$value;
return $self->SUPER::sqrt(@_); } # # end of subclass # package main; ########################### Context("Numeric")->variables->are( x => ["Real", limits => [0,2]], # only needed if x is used in the square roots ); # # make sqrt() use our subclass # Context()->functions->set(sqrt=>{class=>'my::Function::numeric'}); Context()->flags->set(reduceConstantFunctions=>0); # # Don't allow fractional powers (avoids 1/2 power) # [Could subclass exponentiation to handle that as well] # LimitedPowers::OnlyPositiveIntegers();$expr = "\sqrt{12 x^2}";

$f = Compute("x*sqrt(6)");  Setup: This code is from Davide Cervone (4/25/10). See the discussion simplifying radical expressions for more information. BEGIN_TEXT Simplify $$expr$$ assuming that $$x \geq 0$$. Do not enter fractional exponents.$BR
$BR $$expr$$ = \{ans_rule(20)\} END_TEXT  Main Text: The problem text section of the file is as we'd expect. $showPartialCorrectAnswers = 1;

ANS( $f-> cmp( checker => sub { my ($correct,$student,$ans) = @_;
return 0 if $ans->{isPreview} ||$correct != $student; # # Get parsed formula for student and correct answers #$student = $ans->{student_formula};$correct = $correct->{original_formula} if defined$correct->{original_formula};
#
# check if equal when sqrt's are replaced by 1
#
Context()->flags->set(setSqrt => 1);
delete $correct->{test_values},$student->{test_values};
my $OK = ($correct == $student); Context()->flags->set(setSqrt => 0); # Value::Error("Check to see if your answer is simplified.") unless$OK;
return \$OK;
)
);

ENDDOCUMENT();


Answer Evaluation: Use a custom checker to check that the answers are equivalent and that they are still equivalent when sqrt() is replaced by 1 (so the stuff outside the sqrt() is equal in both).