SOLUTION: heres another radical problem I'm not sure of, can you help check my answer?2+sqrt(5)/4+3sqrt(5) the answer I got was 7+2sqrt(5)/29

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Question 173273: heres another radical problem I'm not sure of, can you help check my answer?2+sqrt(5)/4+3sqrt(5) the answer I got was 7+2sqrt(5)/29
Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, you are correct.
.
+%282%2Bsqrt%285%29%29%2F%284%2B3sqrt%285%29%29+

+%288-6sqrt%285%29%2B4sqrt%285%29-3%285%29%29%2F%2816-9%285%29%29+
+%288-2sqrt%285%29-15%29%2F%2816-45%29+
+%28-2sqrt%285%29-7%29%2F%28-29%29+
+%282sqrt%285%29%2B7%29%2F%2829%29+
+%287%2B2sqrt%285%29%29%2F%2829%29+

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Bsqrt%285%29%29%2F%284%2B3%2Asqrt%285%29%29 Start with the given expression.


Multiply the fraction by %284-3%2Asqrt%285%29%29%2F%284-3%2Asqrt%285%29%29 (which is the conjugate of the denominator)


Combine the fractions.


FOIL the numerator.


FOIL the denominator.


Multiply.


Square sqrt%285%29 to get 5.


%288-6%2Asqrt%285%29%2B4%2Asqrt%285%29-15%29%2F%2816-3%2Asqrt%285%29%2B3%2Asqrt%285%29-45%29 Multiply.


%28-7-2%2Asqrt%285%29%29%2F%28-29%29 Combine like terms.


%287%2B2%2Asqrt%285%29%29%2F%2829%29 Reduce



So %282%2Bsqrt%285%29%29%2F%284%2B3%2Asqrt%285%29%29=%287%2B2%2Asqrt%285%29%29%2F%2829%29.


So you are correct.