Question 86825
Divide the following:
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{{{(18 + sqrt(567))/9}}}
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You can split this into two terms as follows:
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{{{18/9 + sqrt(567)/9}}}
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The term of 18 divided by 9 is equal to 2. This simplifies the problem to:
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{{{2 + sqrt(567)/9}}}
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Note that the denominator of 9 is equal to {{{sqrt(81)}}}. If we replace the 9 with this
radical the problem now becomes:
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{{{2 + sqrt(567)/sqrt(81)}}}
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By the rules of radicals we can put both terms under the same radical sign to convert
the problem to:
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{{{2 + sqrt(567/81)}}}
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and note that 81 goes into 567 exactly 7 times. So replace 567/81 by 7 and the problem
simplifies to:
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{{{2 + sqrt(7)}}}
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Let's check with a calculator.  First, the original problem:
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Square root of 567 = 23.8117618
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Add 18 to this and you get 41.8117618
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Divide this total by 9 and the result is 4.645751311
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Next let's use a calculator to check our answer.
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The square root of 7 is 2.645751311 and if you add 2 to that you get 4.645751311. 
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The two answers agree, so we have a correct solution to the problem.  The original 
problem simplifies to {{{2 + sqrt(7)}}}
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Hope this helps you to understand the original problem a little better.
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