-9^2 = -81

[insufferablefury]

I need a help from maths teachers.

My dc says her teacher taught the children the answer is 81. And when she has done the work on online maths programme, it's wrong obviously.

I have explained, it's -81, since it's really - (92). And to get answer as 81, the question need to be (-9)2, not -9^2. But being not a maths specialist, cannot explain why in a logical way , and the child blatantly believes the teacher, which is a good thing, but not really if the teacher is wrong.

How do you maths teachers explain this to your students?

[cantkeepawayforever]

Noble,

Not until recently (long story)...

[noblegiraffe]

cant What?!! surely there was not someone more qualified...

[impossibletoday]

@insufferablefury

Teachermaths, she knows √ 9 = +/- 3

I couldn't let this pass.
The square root of any (positive) number is positive. The square root of 9 is 3 and nothing else.
However, the roots of the equation x^2 = 9 are x=3 and x= -3 (the negative of the square root of 9)

[DadDadDad]

impossible - I don't think that's quite right either. 3 and -3 are both square roots of 9. You're right that the symbol √ refers to the positive (real) square root, so √9 = 3, but -√9 = -3 is also a square root.

en.wikipedia.org/wiki/Square_root

If we allow ourselves complex numbers, every number apart from zero has two distinct square roots (and three distinct cube roots etc).

[insufferablefury]

Thank you, impossibletoday and DadDadDad. I need to read them, though most goes over my head I assume. But I will definitely try to get it.
I enjoy learning maths, I really wish I paid more attention when I was younger, but still nice to learn something I didn't know.

[impossibletoday]

Definition: The square root of a number is the positive number which if you multiply it by itself gives you than number. But as I said above the negative of that number may well be the root of an equation

[Teachermaths]

@impossibletoday

There was an exam question squareroot symbol 64 which had 2 answer slots and it expected - 8 and 8. I'm struggling to find it now but it was on the new spec somewhere!

[DadDadDad]

I'm not sure where you are getting your definition from, impossible, but the Wikipedia article starts as follows and it reads perfectly in line with how I've always understood the definition:

In mathematics, a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x.[1] For example, 4 and −4 are square roots of 16 because 42 = (−4)^2 = 16. Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √x, where the symbol √ is called the radical sign or radix.

The "cube roots of 1" is a topic when studying complex numbers, where one looks at the properties of the three cube roots. It's natural to talk about numbers having three cube roots, and just as natural to talk about them having two square roots.

[TeenPlusTwenties]

This is interesting.
Is ^1/2 then the same as the square root sign in assuming the positive?

[DadDadDad]

Yes, Teen - non-integer exponents only really work (if you're sticking with real numbers) with positive numbers in the base. If you define (16)(1/2) as -4 then you have to decide if (16)(1/4) is 2 or -2 and you run into an inconsistency. See my jottings in the picture.

[TeenPlusTwenties]

super

[noblegiraffe]

Is the sad face standard mathematical notation?

[DadDadDad]

When I was an undergrad, writing out mathematical proofs, I think writing QED at the end was (in my mind) a bit pretentious, and the standard notation by lecturers was to draw a little box at the end. I tended to draw a smiling face in my notes, so I was using smileys in the early nineties before they became a thing. I was a bit of a trendsetter now I think about it.

[noblegiraffe]

I found myself describing the tombstone at the end of a proof as a ‘mic drop’ to Y12 the other day.

[DadDadDad]

Ha, noble, so this moment was the biggest mic drop in the history of maths:

[Andrew Wiles] gave a lecture a day on Monday, Tuesday and Wednesday with the title "Modular Forms, Elliptic Curves and Galois Representations". There was no hint in the title that Fermat's last theorem would be discussed, Dr. Ribet said. ... Finally, at the end of his third lecture, Dr. Wiles concluded that he had proved a general case of the Taniyama conjecture. Then, seemingly as an afterthought, he noted that that meant that Fermat's last theorem was true. Q.E.D.

[noblegiraffe]

@DadDadDad

Just saw this on twitter and it reminded me of this thread.

[DadDadDad]

"Yeet bish" - nice! Although if I tried to use it, I can picture my DD putting on this face --> "not cool, Dad, not cool..."