Question 78946
Rationalize the denominator

{{{ 5 / (7 - sqrt(14)) }}}

Multiply by {{{ 7 + sqrt(14) }}} on top and bottom to clear out the radical from the denomator.  (Whenever you multiply by {{{C/C}}}, it multiplies by 1, so the value is unchanged - here  we use C = {{{ 7 + sqrt(14) }}}).

I get {{{ (35 + 5 sqrt(14))/(49 - 14) = (35 + 5 sqrt(14)) / 35 = 1 + (sqrt(14)/7) = (7 + sqrt(14)) / 7 }}} so the answer is yes, they are equal.  I hope your teacher did not mark you wrong for putting the 7 on top since they are both perfectly good expressions and equal to each other, and both have the  the denominator rationalized.  Or if it is a bet with your friend or your big sister I hope that she has to give you the M&Ms or whatever.