document.write( "Question 1188466: The radical $\"+sqrt%2894%2Bsqrt%281440%29%29+\"$ can be expressed as $\"+sqrt%28a%29%2Bsqrt%28b%29+\"$ , where $\"+a%3Cb+\"$ . What is the product ab? \n" ); document.write( "

Algebra.Com's Answer #819567 by mccravyedwin(407) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Ikleyn misinterpreted the problem.  This is a common type problem of simplifying\r\n" );
document.write( "expressions involving square roots occurring under square roots.  While she is\r\n" );
document.write( "right that there are an infinite number of values of a and b which would make\r\n" );
document.write( "the equation\r\n" );
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document.write( "true, this is not what is asked for.  What is being asked for is to find two\r\n" );
document.write( "simple numbers, hopefully, positive integers, a and b, which will make the expression\r\n" );
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document.write( "exactly equivalent to a simpler expression in the form\r\n" );
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document.write( "However, instead of doing your homework for you, I'll instead do one exactly\r\n" );
document.write( "step-by-step like yours that you can follow as a model when solving yours. Here\r\n" );
document.write( "is the problem I will do for you that is exactly like yours in every way:\r\n" );
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The radical $\"sqrt%2899%2Bsqrt%282232%29%29+\"$ can be expressed as
\n" ); document.write( " $\"sqrt%28a%29%2Bsqrt%28b%29+\"$ , where $\"a%3Cb\"$ . What is the product ab?

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document.write( "Square both sides:\r\n" );
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document.write( "equation (1):    \r\n" );
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document.write( "In equation (1), set the term WITHOUT a square root on the left equal to the sum\r\n" );
document.write( "of the terms WITHOUT square roots on the right:\r\n" );
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document.write( "In equation (1), set the term WITH a square root on the left equal to the term\r\n" );
document.write( "WITH a square root on the right:\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "  <---answer!\r\n" );
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document.write( "That's the answer you were asked for.  \r\n" );
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document.write( "But in other problems, you WILL be asked to find a and b.  So I will continue\r\n" );
document.write( "to find the values of a and b:\r\n" );
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document.write( "Solve the system of equations:\r\n" );
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document.write( "Solve the first equation for b:\r\n" );
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document.write( "Substitute in the second equation in the system \r\n" );
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document.write( "a-6 = 0;   a-93 = 0\r\n" );
document.write( "  a = 6;      a = 93\r\n" );
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document.write( "For a = 6         For a = 93\r\n" );
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document.write( "Since a < b, we choose a = 6 and b = 93\r\n" );
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document.write( "So the radical expression  can be expressed as \r\n" );
document.write( ", where \r\n" );
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document.write( "Now do yours the exact same way, step-by-step.\r\n" );
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document.write( "Edwin

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