document.write( "Question 90866: simplify: square root of 112 + square root of 28.
\n" ); document.write( "I don't remember the steps to doing this. Can you help? \n" ); document.write( "
Algebra.Com's Answer #65934 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
For this problem you use the rule that says:
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\n" ); document.write( "\"sqrt%28a%2Ab%29+=+sqrt%28a%29%2A+sqrt%28b%29\"
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\n" ); document.write( "Then the trick is to find a value for one of the variables (a or b) that is a perfect
\n" ); document.write( "square.
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\n" ); document.write( "Let's start with 112. After playing with factors of 112 for a while you can come up with
\n" ); document.write( "the factors 16*7. Notice that 16 is a perfect square. And now you can apply the rule:
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\n" ); document.write( "\"sqrt%28112%29+=+sqrt%2816%2A7%29+=+sqrt%2816%29%2Asqrt%287%29\"
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\n" ); document.write( "Then you can take the square root of 16 to get 4. So you can replace the square root of
\n" ); document.write( "16 by 4 and you have \"4%2Asqrt%287%29\". So you have simplified \"sqrt%28112%29\" down to
\n" ); document.write( "\"4%2Asqrt%287%29\".
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\n" ); document.write( "You can next apply the same sort of simplification to \"sqrt%2828%29\". Notice that 28
\n" ); document.write( "can be factored into 4*7 and that 4 is a perfect square. Applying the rule gives:
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\n" ); document.write( "\"sqrt%2828%29+=+sqrt%284%2A7%29+=+sqrt%284%29%2Asqrt%287%29\"
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\n" ); document.write( "Then find the square root of 4 ... which is 2 and replace \"sqrt%284%29\" by 2 to get:
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\n" ); document.write( "\"sqrt%2828%29+=+sqrt%284%2A7%29+=+sqrt%284%29%2Asqrt%287%29+=+2%2Asqrt%287%29\"
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\n" ); document.write( "So we have simplified the second term of the problem down to \"2%2Asqrt%287%29\"
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\n" ); document.write( "Substitute these two into the original problem:
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\n" ); document.write( "\"sqrt%28112%29+%2B+sqrt%2828%29\"
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\n" ); document.write( "becomes
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\n" ); document.write( "\"4%2Asqrt%287%29+%2B+2%2Asqrt%287%29\"
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\n" ); document.write( "Then you can add these two directly to get \"6%2Asqrt%287%29\". If it helps you to visualize
\n" ); document.write( "this step you can factor out \"sqrt%287%29\" from the two terms and get:
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\n" ); document.write( "\"%284+%2B+2%29%2Asqrt%287%29\"
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\n" ); document.write( "and then just add the two numbers in the parentheses to get \"6%2Asqrt%287%29\".
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\n" ); document.write( "You can quickly verify this on a calculator. The square root of 112 is 10.58300524 and
\n" ); document.write( "the square root of 28 is 5.291502622. And if you add these two together (as the original problem
\n" ); document.write( "called for) you get 15.87450786.
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\n" ); document.write( "Then take the answer \"6%2Asqrt%287%29\". Using a calculator you find that \"sqrt%287%29\" is
\n" ); document.write( "2.645751311. Multiply that by 6 and you have 15.87450787. Close enough to the other way.
\n" ); document.write( "The error in the very last decimal place is caused by the calculator rounding off.
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\n" ); document.write( "Hope this helps you to understand the problem and a method you can use to do it.\r
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