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If we write sqrt(2) + sqrt(3) + 1/(2*sqrt(2) + 3*sqrt(3)) in the form (a*sqrt(2) + b*sqrt(3))/c such that a, b, and c are positive integers and c is as small as possible, then what is a + b + c?

 Nov 18, 2022
 #1
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Simplify:  sqrt(2) + sqrt(3) + 1/(2*sqrt(2) + 3*sqrt(3))

 

Multiply both the numerator and the denominator by:

1/(2*sqrt(2) + 3*sqrt(3)) and factor

 

 (17 sqrt(2) + 22 sqrt(3)) / 19

 Nov 18, 2022

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