/sci/ - Science & Math

I thought everyone just...knew the sqrt of 144 was 12?

anyway, if you are failing at finding roots, consider the last digit. There are relatively few numbers that similarly multiply and get the same last digit.

aka, the sqrt of 144
4 is the last digit. 2x2 is 4, so the root must end in 2. If you are doing a non-calculator it is almost certainly an integer.
process of elimination by looking at the size of the number.

2x2 is obviously too small
next you have 12 and 22 and at a first glance it could be either. then approximate.

10x10 = 100, just combine the zeroes
20x20 = 2x2(first digits) = 4
then 10x10 = 100, then multiply the numbers together = 400.

you can now approximate that 100 is much closer to 144 than 400. So the root must be 12

eg, some large number (common square) 3364
find the last digit (4), thgen list the numbers that end in 4 as multiples of eachother

2x2=4
8x8=6(4)
here you have 2 possibilities
now find the tens unit to approximate

10x10= 100
20x20 = (2x2)(10x10)= 400
30x30= (3x3)(10x10)=900
40x40= (4x4)(10x10)=1600
50x50=(5x5)(10x10)=2500
60x60=(6x6)(10x10)=3600

now consider the unit digit and the size of the approximation of the tens. we can see 60x60 is larger than 3364 and the next down (50x50) with the units included (58x58) is fairly close to 60x60, So the answer must be 58

Why doesn't there exist a set whose cardinality is larger than that of the natural numbers but smaller than that of the reals?

>>1138696
> I can't read
too bad bro, hard to hang in /sci/ like that I'm sure. Maybe try picking up some elementary material to practice on your off time?

>>1019990
> spin is a vector
like time?