Question 1132316
Express {{{(7sqrt(2)+3sqrt(3))/(4sqrt(2)-2sqrt(3))}}} 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, {{{(4sqrt(2)+2sqrt(3))}}}
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= {{{(4sqrt(2)+2sqrt(3))*(7sqrt(2)+3sqrt(3))/((4sqrt(2)+2sqrt(3))*(4sqrt(2)-2sqrt(3)))}}}
= {{{(4sqrt(2)+2sqrt(3))*(7sqrt(2)+3sqrt(3))/(16*2 - 4*3)}}}
= {{{(4sqrt(2)+2sqrt(3))*(7sqrt(2)+3sqrt(3))/(20)}}}
= {{{(2sqrt(2)+sqrt(3))*(7sqrt(2)+3sqrt(3))/(10)}}}
= {{{(14*2 + 3*3 + 6sqrt(6) + 7sqrt(6))/10}}}
= {{{(37 + 13sqrt(6))/10}}}
= {{{3.7 + 1.3sqrt(6)}}}