A surd simplification masterclass | Colin

The estimable @solvemymaths tweeted, some time back:
hmm, perhaps I’ll keep this one as “sin(22)” http://pic.twitter.com/cT5IHonoyb

— solve my maths (@solvemymaths) January 16, 2016

A sensible option? Perhaps. But Wolfram Alpha is being a bit odd here: that’s something that can be simplified significantly. (One aside: I’m not convinced that actually is $\sin(22º)$, because I get a different answer in the first line, and WA doesn’t give an exact answer for it — but I’m willing to be corrected! So I’m going to call it $S$ instead of $\sin(22º)$)

Before I do anything, I’ll reiterate my Key…

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