SOLUTION: How do you deal with square roots within square roots, for example sqrt(4 + 2sqrt3)/sqrt2? Thank you for your help!

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Question 87556: How do you deal with square roots within square roots, for example
sqrt(4 + 2sqrt3)/sqrt2?
Thank you for your help!
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
It doesn't happen very often, but let's try it. Just remember to obey the rules, and don't make up new rules that aren't true for all real numbers. What we know is that you can multiply sqrt%28a%29%2Asqrt%28b%29=sqrt%28ab%29 provided a and b are NOT both negative. Also, you know that rationalizing the denominator is always a good place to start:


Now, be really careful not to change the rules or make up "new" ones!
+%28sqrt%282%29%29%2Asqrt%284%2B2%28sqrt%283%29%29%29%2F2
%28sqrt%288+%2B+4sqrt%283%29%29%29%2F2+
+%28sqrt%284%282%2Bsqrt%283%29%29%29%29%2F2+
+%28sqrt%284%29%2Asqrt%282%2Bsqrt%283%29%29%29%2F2+
+%282%2Asqrt%282%2Bsqrt%283%29%29%29%2F2+
+sqrt%282%2Bsqrt%283%29%29+
Now, I know this is correct because I checked it with my calculator. However, there may be something else that can be done to eliminate the square root of the square root. I remember doing something like this about 20 years ago in trigonometry, but I haven't worked with it in a very long time. Therefore, if you want a second opinion, go ahead and post the question again, and see if someone else has some ideas about it.

This is a very interesting problem!!

R^2 Retired from SCC