Algebra.Com's Answer #793926 by ikleyn(52943)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Prove that if a, b, and c are the sides of a triangle, then so are sqrt(a), sqrt(b), and sqrt(c).
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document.write( " Proof\r
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document.write( "Let assume that \r\n" );
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document.write( "  +  <=  . (1)\r\n" );
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document.write( "where \"a\", \"b\" and \"c\" are the sides of a triangle.\r\n" );
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document.write( "I want to lead it to CONTRADICTION.\r\n" );
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document.write( "Indeed, square both sides of (1). You will get\r\n" );
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document.write( " a +  + b <= c, or\r\n" );
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document.write( " a + b <= c - .\r\n" );
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document.write( "Then even more so\r\n" );
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document.write( " a + b < c.\r\n" );
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document.write( "But it contradicts to the triangle inequality a + b > c.\r\n" );
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document.write( "Thus we proved that a + b > c IMPLIES + > .\r\n" );
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document.write( "It works for any combinations of sides of a triangle.\r\n" );
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document.write( "Thus we proved that the values , , satisfy all triangle inequalities,\r\n" );
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document.write( "if \"a\", \"b\" and \"c\" are the sides of a triangle.\r\n" );
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document.write( "It implies that if \"a\", \"b\" and \"c\" are the sides of a triangle, then , , and form a triangle, too.\r\n" );
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document.write( " S O L V E D\r
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