
Bases
Hi all.
I simply want to know what is the best way to do sums in different bases. Base 10 is easy and we can all do sums with it but what if I had 342  173. In base 10 the answer is 169. Fine. But how would I go about solving it in base 9 or 8? What difference, in my mind, do I need to apply to make it easier to do?
I have worked out that 169 in Base 9 is 207 and in Base 8 is 251 but I had to find the answer in Base 10 and then convert it and that just takes ages. There must be a simplier way.
Also, If anyway can find the thread about working out square roots without a calculator I would be grateful.

342[8]  173[8] = 147[8]
Do it like:
342
 173

Instead of "borrowing" 10, borrow 8. Instead of bumping a digit at 10, bump at 8.
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Newtons Approximation for Square Root

paultwant is, of course, completely correct you add and subtract in other bases exactly like you do in base 10 except that you "carry" or "borrow" the base rather than 10.
A little more detail:
342 173 (base 9)
Since "2" is smaller than "3" we "borrow 9: 9+ 2= 11 and 11 3= 8 so we write "8" in the first place.
Since we "borrowed", we now have "3" rather than "4" in the second place (9 is 10 in base 9). 7 is larger than 3 we borrow again: 9+3= 12 and 12 7= 5 so we write "5" in the second place.
Since we "borrowed", we now have "2" rather than "1" in the third place. 2 1= 1 so we write "1" in the third place.
In base 9, 342 173 is 158.