SOLUTION: Rationalize -(2/sqrt(2-sqrt(3))

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Question 1057035: Rationalize -(2/sqrt(2-sqrt(3))

Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
-2%2Fsqrt%282-sqrt%283%29%29
=
= %28-2%2A%28sqrt%282-sqrt%283%29%29%29%29%2F%282-sqrt%283%29%29+
=
=
(denominator is 1)
= +%28-2%2A%28sqrt%282-sqrt%283%29%29%29%2A%282%2Bsqrt%283%29%29%29+

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Rationalize -(2/sqrt(2-sqrt(3))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

-2%2Fsqrt%282-sqrt%283%29%29 =  = -%282%2Asqrt%282%2Bsqrt%283%29%29%29%2Fsqrt%282%5E2-%28sqrt%283%29%29%5E2%29 = -%282%2Asqrt%282%2Bsqrt%283%29%29%29%2Fsqrt%281%29 = -%282%2Asqrt%282%2Bsqrt%283%29%29%29%2F1 = -2%2Asqrt%282%2Bsqrt%283%29%29.

For closely related lessons see
    - HOW TO rationalize a fraction by making its denominator free of square roots
    - HOW TO rationalize a fraction by making its denominator free of cubic roots
    - Amazing calculations with fractions that contain quadratic irrationalities in denominators
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Simplifying and rationalizing expressions and functions (denominators)".