document.write( "Question 1208935: True or false? If a and b are both irrational then a*b must always be irrational? \n" ); document.write( "

Algebra.Com's Answer #847468 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "Answer: False\r
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\n" ); document.write( "\n" ); document.write( "Reason:
\n" ); document.write( "We just need one counter-example to disprove the claim. Through a bit of trial and error we can generate this $\"sqrt%2820%29%2Asqrt%285%29+=+sqrt%2820%2A5%29+=+sqrt%28100%29+=+10\"$ \r
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\n" ); document.write( "\n" ); document.write( "The $\"sqrt%2820%29\"$ and $\"sqrt%285%29\"$ are each irrational since they individually cannot be expressed as a fraction of two integers.
\n" ); document.write( "But the result 10 = 10/1 is rational since it can be written as a ratio of integers 10 over 1.\r
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\n" ); document.write( "\n" ); document.write( "This disproves the template irrational*irrational = irrational as there are some exceptions. \r
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\n" ); document.write( "\n" ); document.write( "Note that irrational*irrational = rational is false as well (try $\"a+=+sqrt%282%29\"$ and $\"b+=+sqrt%283%29\"$ to see what happens).
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