SOLUTION: How would you solve these? I think you would rationalize the denominator first, is that right? These are two radical problems. {{{ 2 / (sqrt(3)-sqrt(5)) }}} {{{ 2 / sqrt(6)

Algebra ->  Radicals -> SOLUTION: How would you solve these? I think you would rationalize the denominator first, is that right? These are two radical problems. {{{ 2 / (sqrt(3)-sqrt(5)) }}} {{{ 2 / sqrt(6)      Log On


   



Question 612834: How would you solve these? I think you would rationalize the denominator first, is that right? These are two radical problems.
+2+%2F+%28sqrt%283%29-sqrt%285%29%29+
+2+%2F+sqrt%286%29+%2B+%283%2F4%29+
Thank you!!!!!

Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
+2+%2F+%28sqrt%283%29-sqrt%285%29%29+
------
Multiply numerator and denominator by (sqrt(3)+sqrt(5)) to get:
-------
= [2(sqrt(3)+sqrt(5))]/ [3-5]
----
= -(sqrt(3)+sqrt(5))
============================
Ratioalize the denominator of the 1st fraction:
[2sqrt(6)/6] + [3/4]
------
= sqrt(6)/3 + 3/4
-----
-----
= [4sqrt(6) + 3*3]/12
----
= [4sqrt(6)+9]/12
=======================
cheers,
Stan H.





Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How would you solve these? I think you would rationalize the denominator first, is that right? These are two radical problems.
---------------
There's nothing to solve, no variable.
+2+%2F+%28sqrt%283%29-sqrt%285%29%29+
Multiply the NUM and DEN by the conjugate of the DEN %28sqrt%283%29%2Bsqrt%285%29%29
= +2%28sqrt%283%29%2Bsqrt%285%29%29+%2F+%283+-+5%29
= -sqrt%283%29+-+sqrt%285%29
--------------------------------------
+2+%2F+sqrt%286%29+%2B+%283%2F4%29+
=+2sqrt%286%29+%2F6+%2B+%283%2F4%29
=+4sqrt%286%29+%2F12+%2B+%289%2F12%29
= %284sqrt%286%29+%2B+9%29%2F12