SOLUTION: Help! :-( I am having trouble solving this problem. It is a homework assignment due Tuesday! Thank you so very much!! Please show the steps on how to solve also. Thanks!! Rationali

Algebra ->  Radicals -> SOLUTION: Help! :-( I am having trouble solving this problem. It is a homework assignment due Tuesday! Thank you so very much!! Please show the steps on how to solve also. Thanks!! Rationali      Log On


   



Question 81042: Help! :-( I am having trouble solving this problem. It is a homework assignment due Tuesday! Thank you so very much!! Please show the steps on how to solve also. Thanks!! Rationalize the denominator:
5/(sqrt6)+(sqrt5)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Help! :-( I am having trouble solving this problem. It is a homework assignment due Tuesday! Thank you so very much!! Please show the steps on how to solve also. Thanks!! Rationalize the denominator:

5%2F%28sqrt%286%29%2Bsqrt%285%29%29
Form the conjugate of the denominator,
The conjugate of a two-term expression
has the same first term, but the second
term has its sign changed. So the
conjugate of sqrt%286%29%2Bsqrt%285%29 is
sqrt%286%29-sqrt%285%29. So put this over
itself like this %28sqrt%286%29-sqrt%285%29%29%2F%28sqrt%286%29-sqrt%285%29%29
which just equals to 1. Now multiply the
original expression by that:
5%2F%28sqrt%286%29%2Bsqrt%285%29%29%28sqrt%286%29-sqrt%285%29%29%2F%28sqrt%286%29-sqrt%285%29%29
Now put parentheses around every expression with two terms:
5%2F%28%28sqrt%286%29%2Bsqrt%285%29%29%29%28%28sqrt%286%29-sqrt%285%29%29%29%2F%28%28sqrt%286%29-sqrt%285%29%29%29
Put it all as just one fraction

Distribute out the top, and FOIL out the bottom:

Notice that sqrt%286%29%2Asqrt%286%29=6, sqrt%285%29%2Asqrt%285%29=5, sqrt%286%29%2Asqrt%285%29=sqrt%2830%29, and sqrt%285%29%2Asqrt%286%29=sqrt%2830%29

+%285%2Asqrt%286%29+-+5%2Asqrt%285%29%29%2F%286-sqrt%2830%29%2Bsqrt%2830%29-5%29%29
The two radical terms in the bottom cancel out and we just have
+%285%2Asqrt%286%29+-+5%2Asqrt%285%29%29%2F%286-5%29%29
or just
+%285%2Asqrt%286%29+-+5%2Asqrt%285%29%29%2F1%29
or just
+5%2Asqrt%286%29+-+5%2Asqrt%285%29%29