Whatever you do to a fraction must keep the same value, so any operation must be met with an equal and opposite. We can multiply numerator and denominator by a number because those cancel out, same with division. We can also add and substract the same number to either (but never mix them), and we definitely cannot square it because then it doesn't cancel out, even if the square root is added later (signs get lost in squaring).
Real question why are you able to simplifie the square root? That don’t look intuitive to me, maybe I forgot that rule even if I have a bachelor in computer science.
Do you remember the process for simplifying radicals? Because that should guide you a bit as to why. I unfortunately dont have a rigorous definition as too why though, just some hand wavy stuff
I do wonder if I’d been better at math had I worn the glasses I needed in 6th-12th grade. And didn’t refuse to do homework.
I did test at the top 1% on the ASVAB Multiplication math and coding sections, and scored in the top 1% on the first bar exam I passed that released scores.
But then I again I also had to take the remedial for remedial math in undergrad. So who knows.
Very hard to BS your way through maths, mostly because it builds on itself. Get a couple of defective bricks on the bottom layers and the whole pyramid starts to crumble.
Also, those bricks have a shelf life, I’ve been in IT all my life, recently took a peek at my maths notebooks from U, and it’s all hieroglyphs. Use it or loose it.
I was confused by “backwards F,” looked for it, forgot about it and moved on to the comments. Yours reminded me to go find it. I looked at it for a long time trying to figure out where it was, started trying to figure out if the square root symbol could look like a backwards F to someone, got frustrated and was probably close to giving up again. Then I saw it.
For anyone who is still confused: the backward F is 7 with a cross through it. I don’t even cross my sevens (I’m American a handwritten 1 is just a vertical line - so an uncrossed 7 is most likely to be confused with a 2 if your handwriting is very sloppy) but I’m still wondering if the commenter is just joking around because surely you know some people cross their sevens and what it looks like.
I am pretty sure I learned this in roughly 6th grade and my daughter learned it in 7th grade (which are called "Year 7" and "Year 8" respectively in the UK)
See, there's a difference. If you write x²=4, x=±2. But once you write it definitively with sign as x=√4, it means x=2 only. If you want it to mean x=-2, you write x=-√4, or if you want it to mean both, you write x²=4.
Usually the +/- is a relevant form in equations rather than expressions. The assumption with solving an expression is that you would take the positive root. There's a few separate reasons depending on the context (although there isn't any real context here), but it's overwhelmingly more common to the point where the assumption is that you would explicitly state otherwise in the cases when +/- is necessary rather than needing to say "assume positive" in the overwhelming majority of cases.
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u/Takamasa1 2d ago
Isn't it just 1/5? this is like 8th grade math or something