Question 457246
The general rule of thumb is that you do not leave a radical in the denominator.
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In this problem, you can begin by changing the {{{sqrt(1/2)}}} to its equivalent form:
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{{{sqrt(1)/sqrt(2)}}}
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When you substitute this into the original expression, it becomes:
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{{{sqrt(2)+sqrt(1)/sqrt(2)}}}
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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(2)/sqrt(2)}}} as follows:
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{{{sqrt(2)*sqrt(2)/sqrt(2)+sqrt(1)/sqrt(2)}}}
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Multiplying out the numerator in the first term {{{sqrt(2)*sqrt(2)}}} results in just 2. When you substitute this the expression becomes:
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{{{2/sqrt(2)+sqrt(1)/sqrt(2)}}}
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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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{{{(2+sqrt(1))/sqrt(2)}}}
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But {{{sqrt(1)=1}}} and this can be substituted into the expression to get:
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{{{(2+1)/sqrt(2)}}}
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And performing the addition in the numerator results in:
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{{{3/sqrt(2)}}}
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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(2)/sqrt(2)}}}.
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{{{(3/sqrt(2))*(sqrt(2)/sqrt(2))}}}
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The numerator becomes {{{3*sqrt(2)}}} and the denominator is {{{sqrt(2)*sqrt(2)}}} which multiplies out to 2.  Substituting these two results into the expression gives:
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{{{(3*sqrt(2))/2}}}
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And that is the answer.
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Hope this helps you to understand the problem.