Question 163585
I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth. 
11
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√7 + 8 
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Use the "conjugate" to get rid of radicals in the DEN.  Multiply NUM and DEN by {{{sqrt(7)- 8}}}
[11*(sqrt(7) -8]/(7 - 64)
= -{{{(11*sqrt(7) - 8)/57}}}
Multiplying by the "conjugate" is something you'll see more of to deal with radicals and imaginaries.

and 
3
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2√5 - √7 
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Same approach, multiply by {{{2sqrt(5) + sqrt(7)}}}
= {{{3*(2sqrt(5) + sqrt(7))/(20 - 7)}}}
= {{{(6sqrt(5) + 3sqrt(7))/13}}}