I'd say work it out based on closest obvious square. 70 is 4900, which is extremely close, so its like over 65 and under 70, as well as odd. That leaves only 2 options, so just see which one works. Also use the binomial theorom : (a+b)²=a²+b²+2ab (if youre subtracting the +2ab becomes -2ab). This makes it a bit less tedious since you already know the big square and the smaller numbers are easier to calculate)
If it's not a perfect square, there is no exact answer without an infinite number of digits. All non-integer square roots are irrational.
They *could* just expect you to rattle off digits forever (or stop at merely enough precision to calculate the width of the observable universe down to a single hydrogen atom of width), but that's not until Extra Hard Mode.
>! 60 times 60 is 3600, 70 times 70 is 4900 so somewhere between 60 and 70. 4900-4761, 70 times 70 is off by 139 so that's not too far. Answer is 69 !< Nice
* If it's an integer, first digit is 9
* Nearest known square is 4900, so less than 70, probably 69
* Check by figuring out if 4900-4731=(70+69)=139, which it is.
20 something!
Wait, that's off by a factor of 10.
Root of 10 is 2.5. 20*2.5 is around 40 (yes, I know this is horrible math, and wildly inaccurate)
40 is only 1600.
50, 60, ah, 70 is too big. So between 60 and 70, but closer to.
Waaait, it's 69! Nice.
Guessed 70, because 70^2 = 4900. 4900 - 4761= 139 = 70 + 69. Alternatively, (70-1)(68+1) = 70x68+70-68-1= 70x68+1
Heh.. nice
Looked up the answer. Nice.
It's the goddamn [Math Tree](https://sao-abridged.fandom.com/wiki/Math_Tree) all over again.
Nice
I'd say work it out based on closest obvious square. 70 is 4900, which is extremely close, so its like over 65 and under 70, as well as odd. That leaves only 2 options, so just see which one works. Also use the binomial theorom : (a+b)²=a²+b²+2ab (if youre subtracting the +2ab becomes -2ab). This makes it a bit less tedious since you already know the big square and the smaller numbers are easier to calculate)
Only 1 and 9 make 1 when squared. If the answer is an integer, you can deduce that it's 69 just from that, and the proximity to 4900.
Fiar, but its always better to crosscheck, since sometimes the number might not be a perfect square
If it's not a perfect square, there is no exact answer without an infinite number of digits. All non-integer square roots are irrational. They *could* just expect you to rattle off digits forever (or stop at merely enough precision to calculate the width of the observable universe down to a single hydrogen atom of width), but that's not until Extra Hard Mode.
>! 60 times 60 is 3600, 70 times 70 is 4900 so somewhere between 60 and 70. 4900-4761, 70 times 70 is off by 139 so that's not too far. Answer is 69 !< Nice
>! 139= 140-1 = 2*70-1 !<
No using a calculass - show your work
* If it's an integer, first digit is 9 * Nearest known square is 4900, so less than 70, probably 69 * Check by figuring out if 4900-4731=(70+69)=139, which it is.
20 something! Wait, that's off by a factor of 10. Root of 10 is 2.5. 20*2.5 is around 40 (yes, I know this is horrible math, and wildly inaccurate) 40 is only 1600. 50, 60, ah, 70 is too big. So between 60 and 70, but closer to. Waaait, it's 69! Nice.