document.write( "Question 457246: simplify the expression
\n" ); document.write( " $\"+sqrt%282%29%2B+sqrt%281%2F2%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #313749 by bucky(2189) $\"\"$ $\"About$

You can put this solution on YOUR website!
The general rule of thumb is that you do not leave a radical in the denominator.
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\n" ); document.write( "In this problem, you can begin by changing the $\"sqrt%281%2F2%29\"$ to its equivalent form:
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\n" ); document.write( " $\"sqrt%281%29%2Fsqrt%282%29\"$
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\n" ); document.write( "When you substitute this into the original expression, it becomes:
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\n" ); document.write( " $\"sqrt%282%29%2Bsqrt%281%29%2Fsqrt%282%29\"$
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\n" ); document.write( "To add these two terms together they must both have a common denominator. You can make this happen by multiplying the first term by $\"sqrt%282%29%2Fsqrt%282%29\"$ as follows:
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\n" ); document.write( " $\"sqrt%282%29%2Asqrt%282%29%2Fsqrt%282%29%2Bsqrt%281%29%2Fsqrt%282%29\"$
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\n" ); document.write( "Multiplying out the numerator in the first term $\"sqrt%282%29%2Asqrt%282%29\"$ results in just 2. When you substitute this the expression becomes:
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\n" ); document.write( " $\"2%2Fsqrt%282%29%2Bsqrt%281%29%2Fsqrt%282%29\"$
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\n" ); document.write( "Since both terms have a common denominator, you can now add the numerators and place that sum over the common denominator.
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\n" ); document.write( " $\"%282%2Bsqrt%281%29%29%2Fsqrt%282%29\"$
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\n" ); document.write( "But $\"sqrt%281%29=1\"$ and this can be substituted into the expression to get:
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\n" ); document.write( " $\"%282%2B1%29%2Fsqrt%282%29\"$
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\n" ); document.write( "And performing the addition in the numerator results in:
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\n" ); document.write( " $\"3%2Fsqrt%282%29\"$
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\n" ); document.write( "As stated early in this problem, the usual practice is to not leave a radical in the denominator. You can get rid of the radical in the denominator by multiplying this fraction by $\"sqrt%282%29%2Fsqrt%282%29\"$ .
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\n" ); document.write( " $\"%283%2Fsqrt%282%29%29%2A%28sqrt%282%29%2Fsqrt%282%29%29\"$
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\n" ); document.write( "The numerator becomes $\"3%2Asqrt%282%29\"$ and the denominator is $\"sqrt%282%29%2Asqrt%282%29\"$ which multiplies out to 2. Substituting these two results into the expression gives:
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\n" ); document.write( " $\"%283%2Asqrt%282%29%29%2F2\"$
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\n" ); document.write( "And that is the answer.
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\n" ); document.write( "Hope this helps you to understand the problem. \n" ); document.write( "

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