document.write( "Question 661703: i have a math problem that say \" I am thinking of a number that when multiplied by itself gives me a 3-digit product where the hundreds digit and the ones digit are the same and the tens digit is the sum of the other two digits. what number am i? \n" ); document.write( "

Algebra.Com's Answer #411768 by htmentor(1343) $\"\"$ $\"About$

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Let x = the number
\n" ); document.write( "Let n = the hundreds digit = the ones digit
\n" ); document.write( "Then the tens digit = 2n
\n" ); document.write( "The 3-digit product can be written as
\n" ); document.write( "x^2 = 100n + 10(2n) + n = 121n
\n" ); document.write( "This gives x = 11 $\"sqrt%28n%29\"$
\n" ); document.write( "The product is three digits, and $\"sqrt%28n%29\"$ must be an integer
\n" ); document.write( "If n = 1, x = 11 -> x^2 = 121
\n" ); document.write( "If n = 4, x = 22 -> x^2 = 484
\n" ); document.write( "It seems both of these meet the conditions of the problem, so the possible answers are 11 and 22 \n" ); document.write( "

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