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## Max0815

I am currently preparing for a math competition called MATHcounts. I will be studying, and will not be really active. Thanks for your understanding.

Hello all! I am in 7th grade, and I like math and science. I am taking advanced math courses at school, and I believe that learning math will help me strategize and problem solve in the future. I want to either be an eye doctor, or an ornithologist when I grow up. Birds <3. Science <3.

Currently, I hopefully can be in the next moderator election on the AoPS NU forum. During my free time, I usually like to earn random reputation on MSE/ASE, do some weird math problems, or write some random proofs, prove math is wrong by finding all sorts of false proofs, share my knowledge on astronomy stackexchange, and chat with Daisy via PM on AoPS.

If anyone wants to contact me, please email "maxfang2015@yahoo.com" or "maxfang2016@yahoo.com". I will not be accepting junk or spam, and I rarely check my email, so you may have a long time lag before I reply back, if I decide to, or if it is necessary.

I furthermore want you all to know that MSE site is not a homework mill, and please when you ask a question, add what you have tried along with it, even if it may be a sentence.

My base "graduated" site on Stack Exchange is Math SE, my base beta site is Astronomy SE.

Thanks,

Max0815 Just a small note to myself

$$\sqrt{a+b\sqrt{c}}=?$$

There are the following identities.

$$\sqrt{a+\sqrt{b}}=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}+\sqrt{\frac{a-\sqrt{a^2-b}}{2}}$$ and $$\sqrt{a-\sqrt{b}}=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}-\sqrt{\frac{a-\sqrt{a^2-b}}{2}},$$ where all numbers under radicals are non-negatives.

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