document.write( "Question 447774: how to simplify sqrt (12ab^3c^2) \n" ); document.write( "

Algebra.Com's Answer #853360 by ikleyn(53570) $\"\"$ $\"About$

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\n" ); document.write( "how to simplify sqrt (12ab^3c^2)
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\n" ); document.write( "\n" ); document.write( "        The answer    $\"2bc%2Asqrt%283ab%29\"$   in the post by @mananth is $\"highlight%28highlight%28INCORRECT%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "        The correct answer is    $\"2%2Aabs%28b%29%2Aabs%28c%29%2Asqrt%283%2Aa%2Ab%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "                                E x p l a n a t i o n\r
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document.write( "In problems of this kind, we assume that the variables are real numbers and the expression under the square root\r\n" );
document.write( "is non-negative.\r\n" );
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document.write( "We should understand that c^2 is necessary (always) non-negative, but 'c' itself can be negative.\r\n" );
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document.write( "We also should understand that  ' b '  can be negative (together with b^3), but the product ' a*b^3 '  is necessary non-negative,\r\n" );
document.write( "same as the product  ' ab '.\r\n" );
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document.write( "In the problems of this kind, it is also assumed that the value of the square root itself is also non-negative.\r\n" );
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document.write( "Therefore, when ' b^2 ' goes out the square root, it comes to outside as |b|, the absolute value of  ' b '.\r\n" );
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document.write( "Similarly, when ' c^2 ' goes out the square root, it comes to outside as |c|, the absolute value of  ' c '.\r\n" );
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document.write( "Therefore, the final formula in the answer is as it is shown in my post at the beginning.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly and explained completely.\r
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