Absurd surds and other maths madness

H wanders into the kitchen, maths revision homework in hand, "Mum, what's an irrational number?" she whines in a pleading voice as though I really might have the faintest idea of an answer. The words go in but are then instantly rejected by my right-sided brain.

"Unreasonable numbers that get upset easily," I venture unhelpfully.  She rolls her eyes, sighs deeply and then states the depressing truth:

"You really are of no use at all when it comes to maths," she complains.

To some extent she's right. Now she's 15 years old and building up to national exams I am of little help.  The problem is she's left me behind.  I can do fractions, decimals, even simultaneous equations. Averages do not faze me at all, percentages - no problem, and I know that Pi has nothing to do with pastry or a film involving a boat and a tiger. But this is a foundation level understanding only and H has moved on to inscrutable topics involving tangents and indices.  I cannot bring myself to look at the chapter in her maths textbook entitled 'Algebraic Expressions and Formulae" without feeling quite dizzy. 

In my role as a learning support teacher I often have to think of creative ways to explain mathematical concepts. In the junior school, for instance, there is great job satisfaction to be had when after marching around the edge of the playground a pupil finally understands perimeter or when the mystery of fractions are revealed by cutting up cakes. Even at secondary level I find the idea of a lift and floors below ground level helpful for the concept of negative numbers  (I know, I know, the proper term is 'integers' but what help is that!)  and I have always associated the hypotenuse with a hippopotamus - being the biggest side (ok, ok, the longest side - but you get the idea) *Pythagoras turns over in his grave several times*

My brain is all about words and pictures and I do not make logical connections. When H explains that she is asking about irrational numbers because it is to do with something called 'surds' I am none the wiser. This is an entirely new piece of vocabulary to me and I can't help but think about Serbs instead and have visions of human-sized numbers dressed  up in Serbian national costume running around the Balkans being irrational. I turn to the dreaded textbook which informs me that 'All real numbers are either rational or irrational'.  Are there unreal numbers then?!  I read on: 'Roots of rational numbers which cannot be expressed as rational numbers are called surds.'   Arrhh, all is clear...as mud. Seriously, what on earth does that sentence mean? They may as well have put 'the answer's a lemon' for all the explanation it provides.

I turn to the fountain of all knowledge - Google -  and come across a video on youtube made by some geeky guy in his bedroom. I didn't know that 'maths porn' like this existed and it proves enlightening. He explains in his nasally voice (and helpfully demonstrates on his scientific calculator) that surds are really just 'nasty square roots'.  It doesn't matter that I don't share his opinion that there are nice square roots, I have made progress and H and I solve the first three questions together.  The white wine seems dangerously low though at the end of it and I think it's time we employed the services of a professional, and sober, tutor rather than rely on social media, alcoholic sustenance and my maths-confuddled brain.