document.write( "Question 752418: Wat irrational numba is betwin 2 & 3. \n" ); document.write( "

Algebra.Com's Answer #457728 by KMST(5328) $\"\"$ $\"About$

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Between 2 and 3 there are infinite irrational numbers (and infinite rational numbers too).
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\n" ); document.write( "ONE IDEA:
\n" ); document.write( "If $\"sqrt%28x%29\"$ is between 2 and 3,
\n" ); document.write( "then $\"2%3Csqrt%28x%29%3C3\"$ means that $\"2%5E2%3C%28sqrt%28x%29%29%5E2%3C3%5E2\"$ , which means $\"4%3Cx%3C9\"$
\n" ); document.write( "So $\"highlight%28sqrt%285%29%29\"$ is a solution, and so are
\n" ); document.write( " $\"highlight%28sqrt%286%29%29\"$ , $\"highlight%28sqrt%287%29%29\"$ , and $\"highlight%28sqrt%288%29%29\"$ .
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\n" ); document.write( "FANCIER IDEAS:
\n" ); document.write( "You probably know that $\"pi\"$ is an irrational number that is between 3 and 4.
\n" ); document.write( "So $\"3%3Cpi%3C4\"$ means that $\"2=3-1%3Cpi-1%3C4-1%3C3\"$ .
\n" ); document.write( " $\"highlight%28+pi-1+%29\"$ is another irrational number between 2 and 3.
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\n" ); document.write( "FANCIER:
\n" ); document.write( "You may not know it, but there is an irrational number called $\"e\"$ that is approximately 2.7183.
\n" ); document.write( "It is sort of like $\"pi\"$ in that there is no other way to express it, and to describe it you have to tell a story. However, the story of $\"e\"$ is more complicated than the story of $\"pi\"$ .
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