document.write( "Question 65683: Use the properties for radicals to simplify the espression. Assume all variables represent positive real numbers.\r
\n" ); document.write( "\n" ); document.write( "sqrt 5/3\r
\n" ); document.write( "\n" ); document.write( "This is not a real number correct? Or do I need to divide them like a regular fraction to get:\r
\n" ); document.write( "\n" ); document.write( "1 sqrt2/3? \n" ); document.write( "

Algebra.Com's Answer #46383 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

Use the properties for radicals to simplify the espression. \r\n" );
document.write( "Assume all variables represent positive real numbers.\r\n" );
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document.write( "sqrt 5/3\r\n" );
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document.write( "Yes that IS a real number.  Only when there's a negative number\r\n" );
document.write( "under the radical do you not have a real number.\r\n" );
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document.write( "Checkley71 above only gave you a decimal approximation,\r\n" );
document.write( "but I'm sure your teacher must not have wanted that, but\r\n" );
document.write( "the simplest radical form instead, which is found by\r\n" );
document.write( "rationalizing the denominator:   \r\n" );
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document.write( "     ____\r\n" );
document.write( "    / 5\r\n" );
document.write( "\  / ---\r\n" );
document.write( " \/   3\r\n" );
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document.write( "To rationalize the denominator, choose the smallest\r\n" );
document.write( "integer that you can multiply the denominator 3 by to get\r\n" );
document.write( "a perfect square.  That number is 3, since 3·3 = 9, which is\r\n" );
document.write( "a perfect square.  So we multiply under the radical by 3/3,\r\n" );
document.write( "which will not change the value because 3/3 is just 1, and\r\n" );
document.write( "you don't change the value when you multiply by 1.\r\n" );
document.write( "\r\n" );
document.write( "     ________\r\n" );
document.write( "    / 5   3\r\n" );
document.write( "\  / ---×---\r\n" );
document.write( " \/   3   3\r\n" );
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document.write( "Multiply numerators and denominators:\r\n" );
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document.write( "\r\n" );
document.write( "     _____\r\n" );
document.write( "    / 15\r\n" );
document.write( "\  / ----\r\n" );
document.write( " \/    9\r\n" );
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document.write( "Now we take square roots of the numerator\r\n" );
document.write( "and denominator:\r\n" );
document.write( "    __\r\n" );
document.write( "   Ö15\r\n" );
document.write( "  -----\r\n" );
document.write( "    Ö9\r\n" );
document.write( "                         _\r\n" );
document.write( "Replace the denominator Ö9 by 3\r\n" );
document.write( "\r\n" );
document.write( "    __\r\n" );
document.write( "   Ö15\r\n" );
document.write( "  -----\r\n" );
document.write( "    3\r\n" );
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document.write( "Edwin

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