Neta wrote:
rezoons wrote:
But the unit digit of something rounded is not always the same as the unit digit of the number itself.
Take 7.75. It's unit digit is 7 but if you round it, you get 8.
I'm not sure i follow the logic here.
That's why i pick (√2+ √3)^8. my solution doesn't follow logic when the sing of decimal is over 0.5 because it makes digit goes up like you said
and it should be really close to integer to find right digit answer
Ok, so if i understand your logic.
(√2+ √3)^8 is nearly equal to 2. So you deduce that the unit digit of (√2+ √3)^8x is the unit digit of 2^x
(√2+ √3)^8 is 9602. so (√2+ √3)^8 's digit is 2.
and 2^x 's digit goes 2, 4, 8, 6, 2, 4, 8, 6 .....
so (√2+ √3)^96 is 6.
Problem is (√2+ √3)^16 is aproximately equal to 92198402.03 and it's unit digit is 2 and not 4 according to your reasoning.
So, i still don't understand.
Sorry if i keep insisting but my computer calculate 8 as the unit digit of (√2+ √3)^100 so i'm still not 100% satisfied. I'm really curious about what was Scorpiour's proof.We solved everything by PM. I was wrong. Sorry for all the post in the queue.