SOLUTION: Please help me simplify further. (2+or- the square root of 212/49) / (4/7)

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Question 196631: Please help me simplify further.
(2+or- the square root of 212/49) / (4/7)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2B-sqrt%28212%2F49%29%29%2F%284%2F7%29 Start with the given expression.


%282%2Bsqrt%28212%2F49%29%29%2F%284%2F7%29 or %282-sqrt%28212%2F49%29%29%2F%284%2F7%29 Break up the "plus/minus" to form two separate expressions.


%282%2Bsqrt%28212%29%2Fsqrt%2849%29%29%2F%284%2F7%29 or %282-sqrt%28212%29%2Fsqrt%2849%29%29%2F%284%2F7%29 Break up the square root.


%282%2Bsqrt%28212%29%2F7%29%2F%284%2F7%29 or %282-sqrt%28212%29%2F7%29%2F%284%2F7%29 Take the square root of 49 to get 7


%282%2Bsqrt%284%2A53%29%2F7%29%2F%284%2F7%29 or %282-sqrt%284%2A53%29%2F7%29%2F%284%2F7%29 Factor 212 to get 4*53


%282%2B%28sqrt%284%29%2Asqrt%2853%29%29%2F7%29%2F%284%2F7%29 or %282-%28sqrt%284%29%2Asqrt%2853%29%29%2F7%29%2F%284%2F7%29 Break up the square root.


%282%2B%282sqrt%2853%29%29%2F7%29%2F%284%2F7%29 or %282-%282sqrt%2853%29%29%2F7%29%2F%284%2F7%29 Take the square root of 4 to get 2


%282%2B%282sqrt%2853%29%29%2F7%29%2A%287%2F4%29 or %282-%282sqrt%2853%29%29%2F7%29%2A%287%2F4%29 Multiply by the reciprocal of the second fraction


2%2A%287%2F4%29%2B%28%282sqrt%2853%29%29%2F7%29%2A%287%2F4%29 or 2%2A%287%2F4%29-%28%282sqrt%2853%29%29%2F7%29%2A%287%2F4%29 Distribute



14%2F4%2B%2814sqrt%2853%29%29%2F%2828%29 or 14%2F4-%2814sqrt%2853%29%29%2F%2828%29 Multiply


7%2F2%2Bsqrt%2853%29%2F2 or 7%2F2-sqrt%2853%29%2F2 Reduce


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Answer:


So %282%2Bsqrt%28212%2F49%29%29%2F%284%2F7%29=7%2F2%2Bsqrt%2853%29%2F2 and %282-sqrt%28212%2F49%29%29%2F%284%2F7%29=7%2F2-sqrt%2853%29%2F2