document.write( "Question 112386: Simplify and combine like radicals\r
\n" ); document.write( "\n" ); document.write( "√ 12 - √ 75 \n" ); document.write( "
Algebra.Com's Answer #82031 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given:
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\n" ); document.write( "\"sqrt%2812%29+-+sqrt%2875%29\"
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\n" ); document.write( "Factor each of the terms under the radical signs to get:
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\n" ); document.write( "\"sqrt%284%2A3%29+-+sqrt%2825%2A3%29\"
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\n" ); document.write( "Recognize that the square root of a product of terms is equal to the product of the square
\n" ); document.write( "roots of each of the terms. Applying this rule results in:
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\n" ); document.write( "\"sqrt%284%2A3%29+-+sqrt%2825%2A3%29=+sqrt%284%29%2Asqrt%283%29+-+sqrt%2825%29%2Asqrt%283%29\"
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\n" ); document.write( "But \"sqrt%284%29+=+2\" and \"sqrt%2825%29+=+5\". Make these substitutions and you get:
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\n" ); document.write( "\"sqrt%284%2A3%29+-+sqrt%2825%2A3%29+=+2%2Asqrt%283%29+-+5%2Asqrt%283%29\"
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\n" ); document.write( "Factoring \"sqrt%283%29\" from each of the terms on the right side gives:
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\n" ); document.write( "\"sqrt%284%2A3%29+-+sqrt%2825%2A3%29+=+%282+-+5%29sqrt%283%29\"
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\n" ); document.write( "The terms 2 and -5 inside the parentheses combine to -3 and when this is substituted
\n" ); document.write( "for the parentheses the problem finally reduces to:
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\n" ); document.write( "\n" ); document.write( "\"sqrt%284%2A3%29+-+sqrt%2825%2A3%29+=+-3%2Asqrt%283%29\"
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\n" ); document.write( "So the answer to this problem is \"-3%2Asqrt%283%29\"
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\n" ); document.write( "Hope this helps you to understand the problem and how to proceed to solve it.
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