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You can put this solution on YOUR website!
i did this by brute force because i didn't know any formula that would allow me to find it directly.
\n" ); document.write( "there may be one but i don't know what it is.
\n" ); document.write( "the brute force method used excel.
\n" ); document.write( "i simply multiplied 3456 by numbers starting from 1 and going up and then checked to see if i got a perfect square or not.
\n" ); document.write( "the answer is 6
\n" ); document.write( "3456 * 6 is a perfect square and multiplying by 6 is the smallest integer i could multiply 3456 by before getting a perfect square as the result.
\n" ); document.write( "here's the results of the brute force method.
\n" ); document.write( "
\r\n" ); document.write( "3456 1 58.78775383 \r\n" ); document.write( "3456 2 83.13843876 \r\n" ); document.write( "3456 3 101.8233765 \r\n" ); document.write( "3456 4 117.5755077 \r\n" ); document.write( "3456 5 131.4534138 \r\n" ); document.write( "3456 6 144 this is a perfect square\r\n" ); document.write( "3456 7 155.5377768 \r\n" ); document.write( "3456 8 166.2768775 \r\n" ); document.write( "3456 9 176.3632615 \r\n" ); document.write( "3456 10 185.9032006 \r\n" ); document.write( "3456 11 194.9769217 \r\n" ); document.write( "3456 12 203.646753 \r\n" ); document.write( "3456 13 211.9622608 \r\n" ); document.write( "3456 14 219.9636334 \r\n" ); document.write( "3456 15 227.6839915 \r\n" ); document.write( "3456 16 235.1510153 \r\n" ); document.write( "3456 17 242.3881185 \r\n" ); document.write( "3456 18 249.4153163 \r\n" ); document.write( "3456 19 256.249878 \r\n" ); document.write( "3456 20 262.9068276 \r\n" ); document.write( "3456 21 269.3993318 \r\n" ); document.write( "3456 22 275.739007 \r\n" ); document.write( "3456 23 281.936163 \r\n" ); document.write( "3456 24 288 this is a perfect square\r\n" ); document.write( "3456 25 293.9387691\r\n" ); document.write( "
\n" ); document.write( "if there is a rule, i don't know it, as i said before.
\n" ); document.write( "it's interesting that the next perfect square is multiplying by a multiple of 6, specifically 4 * 6.
\n" ); document.write( "note that 6 by itself is not a perfect square even though 4 by itself is a perfect square.
\n" ); document.write( "no real relationship there that i can figure out.
\n" ); document.write( "if you're looking for a formula to determine the smallest multiple to get a perfect square i don't have it, but you do have your answer is that's all you wanted.
\n" ); document.write( "i did a search of the web and i did find a way to determine it.
\n" ); document.write( "the link i found is here:
\n" ); document.write( "http://answers.yahoo.com/question/index?qid=20090616105542AAKgSOq
\n" ); document.write( "basically, you break the number down into factors and each factor has to be a perfect square.
\n" ); document.write( "if there's a number that's not a perfect square, then that number is the number you have to multiply your original number by in order to get it to be a perfect square.
\n" ); document.write( "applying that concept to your number, we get the following:
\n" ); document.write( "3456 / 144 = 24 which means that:
\n" ); document.write( "3456 = 144 * 24
\n" ); document.write( "144 is a perfect square, but 24 is not.
\n" ); document.write( "we can, however break down 24 into a multiple of perfect squares.
\n" ); document.write( "24 = 2*12 = 3*8 = 4*6
\n" ); document.write( "4 is a perfect square, so we get:
\n" ); document.write( "3456 = 144*4*6
\n" ); document.write( "since 144*4 is equal to 576 and 576 is a perfect square (24*24), we can reduce this to:
\n" ); document.write( "3456 = 576*6
\n" ); document.write( "6 is not a perfect square, but if we multiply it by 6 we will get a perfect square, then that's the smallest we can get.
\n" ); document.write( "this is because:
\n" ); document.write( "6 is not a perfect square but it can be broken down into:
\n" ); document.write( "6 = 2*3 = 1*6 neither of which is a perfect square.
\n" ); document.write( "that makes 6 the smallest multiple of 3456 to get a perfect square.
\n" ); document.write( "brute force method confirms that:
\n" ); document.write( "
\r\n" ); document.write( "6 1 2.449489743 \r\n" ); document.write( "6 2 3.464101615 \r\n" ); document.write( "6 3 4.242640687 \r\n" ); document.write( "6 4 4.898979486 \r\n" ); document.write( "6 5 5.477225575 \r\n" ); document.write( "6 6 6 this is a perfrect square\r\n" ); document.write( "\n" ); document.write( "