SOLUTION: Express (7√(2)+3√(3))/(4√(2)-2√(3)) in the form p+q√r where p, q and r are rational numbers

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Question 1132316: Express (7√(2)+3√(3))/(4√(2)-2√(3)) in the form p+q√r where p, q and r are rational numbers
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Express %287sqrt%282%29%2B3sqrt%283%29%29%2F%284sqrt%282%29-2sqrt%283%29%29 in the form p+q√r where p, q and r are rational numbers
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Multiply the NUM and the DEN by the conjugate of the DEN, %284sqrt%282%29%2B2sqrt%283%29%29
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= %284sqrt%282%29%2B2sqrt%283%29%29%2A%287sqrt%282%29%2B3sqrt%283%29%29%2F%2816%2A2+-+4%2A3%29
= %284sqrt%282%29%2B2sqrt%283%29%29%2A%287sqrt%282%29%2B3sqrt%283%29%29%2F%2820%29
= %282sqrt%282%29%2Bsqrt%283%29%29%2A%287sqrt%282%29%2B3sqrt%283%29%29%2F%2810%29
= %2814%2A2+%2B+3%2A3+%2B+6sqrt%286%29+%2B+7sqrt%286%29%29%2F10
= %2837+%2B+13sqrt%286%29%29%2F10
= 3.7+%2B+1.3sqrt%286%29