SOLUTION: Rationalize the denominator: 7/√[3] – √[2]

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Question 167726: Rationalize the denominator:
7/√[3] – √[2]
Found 3 solutions by nerdybill, CeCe_101, jim_thompson5910:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Not clear whether you mean:
+7%2Fsqrt%283%29+-+sqrt%282%29+
Or
+7%2F%28sqrt%283%29+-+sqrt%282%29%29+
.
I'll assume the later...
.

+7%28sqrt%283%29+%2B+sqrt%282%29%29%2F%283-2%29
+7%28sqrt%283%29+%2B+sqrt%282%29%29%2F1
+7%28sqrt%283%29+%2B+sqrt%282%29%29
+7sqrt%283%29+%2B+7sqrt%282%29

Answer by CeCe_101(1) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
7%2F%28sqrt%283%29-sqrt%282%29%29 Start with the given expression


Multiply both numerator and denominator by the conjugate of the denominator


Combine the fractions.



%287%28sqrt%283%29%2Bsqrt%282%29%29%29%2F%28%28sqrt%283%29%29%5E2-%28sqrt%282%29%29%5E2%29 FOIL (hint: use the difference of squares)


%287%28sqrt%283%29%2Bsqrt%282%29%29%29%2F%283-2%29 Square each value


%287%28sqrt%283%29%2Bsqrt%282%29%29%29%2F%281%29 Combine like terms.


7%28sqrt%283%29%2Bsqrt%282%29%29 Simplify


7%2Asqrt%283%29%2B7%2Asqrt%282%29 Distribute


So 7%2F%28sqrt%283%29-sqrt%282%29%29=7%2Asqrt%283%29%2B7%2Asqrt%282%29