0.00822649 find the positive square root?

√0.00822649
= 0.0907

..........0.-0--9---0---7
........|------------------------
.....9 | 0.00,82,26,49
........|.........81
........-------------------------
..180|...........126
........|...............0
........|------------------------
1807|............12649
........|............12649
........|----------------------#
=>
sqr(0.00822649)=0.0907
without using the calculator.

The square root of 0.00822649 is 
(0.00822649)^1/2=0.0907

This is the most excellent of troll jobs I've seen in a long time. It's not just the number sequence, it's the phrasing. Notice how every response, even rounded, ends in an odd number? That's some Slucky Leven Blevins stuff. Even Ian's answer, which is, hands down the best answer, isn't 100% right simply because of how you phrased it. UGH ARCHER. You could be asking for the inverse of what you seem to be asking and we'd have no way of knowing which is which. 

Also, as it ends in 49, there's a 7 no matter which way you go, there's a 7 somewhere, and 8226.... notice... 8 2... 6... 2... 8-6 = 2, and u got two; one for each, but in opposite scales. Very interesting combo. 

I retort with "What is up?"

Quickie: 0.091 (calculated with mental arithmetic)

sqrt(.00822649)= 0.090691234

Its positive square root is 0.0907

The positive square root of 0.00822649 is 0.0907.

Perhaps you want a method without calculator.
Find x if x^2 = 0.00822649 = 822649/(10^4)^2
Let (900 + t)^2 = 810,000 + 1800t + t^2 = 822,649
t^2 + 1800t – 12649 = 0, note last number is divisible by 7
(t – 7)(t + 1807) = 0, so select t = 7
907^2 = 822,649
x^2 = [907/10^4]^2
x = 0.0907

This is too deep. I can't help

The square root will always be a positive number because the amount you wrote in your title text is a positive number.