document.write( "Question 1165716: 1. Write three irrational numbers between 5.6 and 5.7 (Show your work).
\n" ); document.write( "1. Write three irrational numbers between 3.8 and 3.9 (Show your work).\r
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Algebra.Com's Answer #790335 by Edwin McCravy(20060)\"\" \"About 
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1. Write three irrational numbers between 5.6 and 5.7 (Show your work).
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document.write( "We begin by squaring 5.6 and 5.7\r\n" );
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document.write( "5.6² = 31.36\r\n" );
document.write( "5.7² = 32.49\r\n" );
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document.write( "This means that if we multiply both sides by 100, we get\r\n" );
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document.write( "5.6²(100) = (5.6)(5.6)(10)(10) = (5.6)(10)(5.6)(10) = (56)(56) = 56² = 3136\r\n" );
document.write( "5.7²(100) = (5.7)(5.7)(10)(10) = (5.7)(10)(5.7)(10) = (57)(57) = 57² = 3249\r\n" );
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document.write( "We know that the square root of any integer between two perfect squares is\r\n" );
document.write( "irrational. There are no perfect squares between perfect squares 56²=3136\r\n" );
document.write( "and 57²=3249.  So we pick any three integers between 3136 and 3249 and their\r\n" );
document.write( "square roots will be irrational.\r\n" );
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document.write( "So let's pick, say, 3163, 3193, and 3223 at random between them.\r\n" );
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document.write( "Taking square roots:\r\n" );
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document.write( "√3163 which is approximately 56.24055476...\r\n" );
document.write( "√3193 which is approximately 56.50663678...\r\n" );
document.write( "√3223 which is approximately 56.77147171...\r\n" );
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document.write( "Dividing under the square root by 100 amounts to dividing by 10, so\r\n" );
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document.write( "√31.63 which is approximately 5.624055476...\r\n" );
document.write( "√31.93 which is approximately 5.650663678...\r\n" );
document.write( "√32.23 which is approximately 5.677147171...\r\n" );
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document.write( "All three are irrational.\r\n" );
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document.write( "Now, do the same exact thing with 3.8 and 3.9.\r\n" );
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document.write( "Edwin
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