SOLUTION: I need to rationalize the denominator of 5 over (7- radical 14). I get 1+ (radical 14 over 7). Is this the same as (7 + radical 14) over 7? Since 7/7 is 1, it should be equivalent.

Algebra ->  Radicals -> SOLUTION: I need to rationalize the denominator of 5 over (7- radical 14). I get 1+ (radical 14 over 7). Is this the same as (7 + radical 14) over 7? Since 7/7 is 1, it should be equivalent.      Log On


   

Question 78946: I need to rationalize the denominator of 5 over (7- radical 14). I get 1+ (radical 14 over 7). Is this the same as (7 + radical 14) over 7? Since 7/7 is 1, it should be equivalent.
Found 2 solutions by mathdoc314, fetter6:
Answer by mathdoc314(58) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator
+5+%2F+%287+-+sqrt%2814%29%29+
Multiply by +7+%2B+sqrt%2814%29+ on top and bottom to clear out the radical from the denomator. (Whenever you multiply by C%2FC, it multiplies by 1, so the value is unchanged - here we use C = +7+%2B+sqrt%2814%29+).
I get 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.



Answer by fetter6(6) About Me  (Show Source):
You can put this solution on YOUR website!
Problem: Rationalize 5%2F%287-sqrt%2814%29%29
Multiple the top and bottom by the conjugate of 7-sqrt%2814%29 which is 7%2Bsqrt%2814%29.
5%2F%287-sqrt%2814%29%29+%2A+%287%2Bsqrt%2814%29%29%2F%287%2Bsqrt%2814%29%29
The numerator becomes 5%287%2Bsqrt%2814%29%29=35%2B5sqrt%2814%29
The denominator becomes %287-sqrt%2814%29%29%287%2Bsqrt%2814%29%29=49-14=35
So the problem reduces to:
%2835%2B5sqrt%2814%29%29%2F35=1%2Bsqrt%2814%29%2F7. So you are correct!
QED