Express 6√245+3√125+4√5 in the form where A and C are relatively prime integers, C is positive, and B is not divisible by the square of any prime. Find A+B+C .
Note that
sqrt (245) = sqrt ( 49 * 5) = 7sqrt (5) and
3sqrt (125) = 3 sqrt ( 25 * 5 ) = 15 sqrt (5)
So....the denominator is just 7sqrt (5) + 15sqrt (5) + 4sqrt (5) = 26sqrt (5)
So we have
6 3 sqrt (5) 3sqrt (5)
_________ = _________ _______ = ____________
26sqrt (5) 13sqrt (5) sqrt (5) 65
√245=7√5
3√125=15√5
This means the denominator can be simplified to:
(7+15+4)√5=26√5
Which means the entire fraction is:
626√5=313√5=3√565