document.write( "Question 106017: The 3-digit number is a perfect square less than 200. If the digits are reversed, the resulting number is also a perfect square. What is the number such that no digits are the same? \n" ); document.write( "

Algebra.Com's Answer #77145 by Fombitz(32388) $\"\"$ $\"About$

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3 digit number less than 200
\n" ); document.write( " $\"100%3C=N%5E2%3C200\"$
\n" ); document.write( "Let’s look at the possible perfect squares in this range
\n" ); document.write( " $\"10%5E2=100\"$
\n" ); document.write( " $\"11%5E2=121\"$
\n" ); document.write( " $\"12%5E2=144\"$
\n" ); document.write( " $\"13%5E2=169\"$
\n" ); document.write( " $\"14%5E2=196\"$
\n" ); document.write( "Let’s look at those squares with digits reversed
\n" ); document.write( "001 – Perfect square $\"%281%5E2%29\"$
\n" ); document.write( "121 – Perfect square $\"%2811%5E2%29\"$
\n" ); document.write( "441 – Perfect square $\"%2821%5E2%29\"$
\n" ); document.write( "961 - Perfect square $\"%2831%5E2%29\"$
\n" ); document.write( "691 – Not a perfect square
\n" ); document.write( "There are four matches 100, 121, 144, and 169 that work.
\n" ); document.write( "However you also mentioned that no two digits can be the same.
\n" ); document.write( "That leaves only 169 as the final answer.
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