document.write( "Question 314204: radical 250 x^5 y^3 \n" ); document.write( "
Algebra.Com's Answer #224601 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's solution is incorrect. He must have mistook\r\n" );
document.write( "250 for 2500.\r\n" );
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document.write( "Later: He came back and fixed it!\r\n" );
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document.write( "\"sqrt%28250x%5E5y%5E3%29\"\r\n" );
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document.write( "250 is not a perfect square but it can be broken up into a perfect square\r\n" );
document.write( "times a non-perfect square, for it can be broken up into 25*10, where 25 \r\n" );
document.write( "is a perfect square and 10 is a non-perfect square. so write 250 as 25*10.\r\n" );
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document.write( "\"sqrt%28red%2825%29%2A10x%5E5y%5E3%29\"\r\n" );
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document.write( "\"x%5E5\" is not a perfect square but it can be broken up into a perfect square\r\n" );
document.write( "times a non-perfect square, for it can be broken up into \"x%5E4%2Ax\", where \"x%5E4\"\r\n" );
document.write( "is a perfect square and \"x\" is a non-perfect square. so write \"x%5E5\" as \"x%5E4%2Ax\".\r\n" );
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document.write( "\"sqrt%28red%2825%29%2A10red%28x%5E4%29%2Ax%2Ay%5E3%29\"\r\n" );
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document.write( "\"y%5E3\" is not a perfect square but it can be broken up into a perfect square\r\n" );
document.write( "times a non-perfect square, for it can be broken up into \"y%5E2%2Ay\", where \"y%5E2\"\r\n" );
document.write( "is a perfect square and \"y\" is a non-perfect square. so write \"y%5E3\" as \"y%5E2%2Ay\".\r\n" );
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document.write( "\"sqrt%28red%2825%29%2A10red%28x%5E4%29%2Ax%2Ared%28y%5E2%29%2Ay%29\"\r\n" );
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document.write( "Notice that I've colored all the perfect squares red. We can take their square\r\n" );
document.write( "roots.\r\n" );
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document.write( "The square root of 25 is 5, so we can take out the 25 as a 5 in front of\r\n" );
document.write( "the radical.\r\n" );
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document.write( "\"red%285%29sqrt%2810red%28x%5E4%29%2Ax%2Ared%28y%5E2%29%2Ay%29\"\r\n" );
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document.write( "The square root of \"x%5E4\" is \"x%5E2\", so we can take out the \"x%5E4\" as\r\n" );
document.write( "an \"x%5E2\" in front of the radical.\r\n" );
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document.write( "\"red%285x%5E2%29sqrt%2810x%2Ared%28y%5E2%29%2Ay%29\"\r\n" );
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document.write( "Finally the square root of \"y%5E2\" is \"y\", so we can take out the \"y%5E2\" as just \r\n" );
document.write( "\"y\" in front of the radical.\r\n" );
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document.write( "\"red%285x%5E2y%29sqrt%2810xy%29\".\r\n" );
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document.write( "Edwin
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