SOLUTION: How can you write expression with rationalized denominator? Squareroot3-squareroot6. / squareroot3+square root6

Algebra ->  Test -> SOLUTION: How can you write expression with rationalized denominator? Squareroot3-squareroot6. / squareroot3+square root6      Log On


   

Question 678278: How can you write expression with rationalized denominator?
Squareroot3-squareroot6. / squareroot3+square root6
Found 2 solutions by stanbon, pmatei:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
write expression with rationalized denominator?
Squareroot3-squareroot6. / squareroot3+square root6
-----------------------
= (sqrt(3)-sqrt(6)) / (sqrt(3)+sqrt(6))
----------------------------------------
Multiply numerator and denominator by sqrt(3)-sqrt(6)
----------------------
= [(sqrt(3)-sqrt(6))(sqrt(3)-sqrt(6))] /[3-6]
------
= [3 - 2sqrt(18) +6] / (-3)
------
= [9-6sqrt(2)] / (-3)
------
= [-3 + 2sqrt(2)]
====================
Cheers,
Stan H.
===========

Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
You take advantage of %28a%2Bb%29%28a-b%29=a%5E2-b%5E2, by considering your denominator as either %28a%2Bb%29 or %28a-b%29 and multiplying both numerator and denominator with the other paranthesis in the formula:
In your case the denominator is the %28a%2Bb%29, thus you multiply with %28a-b%29=%28sqrt%283%29-sqrt%286%29%29:

%28sqrt%283%29-sqrt%286%29%29%5E2%2F%283-6%29
%283-2sqrt%2818%29%2B6%29%2F%28-3%29
%289-6sqrt%282%29%29%2F%28-3%29
-3%2B2sqrt%282%29