eg, in=&70:out=&72
.sqr :\ On entry, !in=input value
LDY #1:STY out+0:DEY:STY out+1 :\ Initialise out to first subtrand
.sqr_loop :\ Repeatedly subtract increasing
SEC :\ odd numbers until in<0
LDA in+0:TAX:SBC out+0:STA in+0 :\ in=in-subtrand, remainder in X
LDA in+1:SBC out+1:STA in+1
BCC sqr_done :\ in<0, all done
INY :\
LDA out+0:ADC #1:STA out+0 :\ step +2 to next odd number
BCC sqr_loop :\ no overflow, subtract again
INC out+1:BNE sqr_loop :\ INC high byte and subtract again
.sqr_done
STY out+0:STX out+1 :\ out?0=root, out?1=remainder
RTS
:
This works by counting how many times increasing odd numbers
can be subtracted until there's nothing left.
For example:
32-1=31 -> 31-3=28 -> 28-5=23 -> 23-7=16 -> 16-9=7 -> 7-11<0
1 2 3 4 5
-> SQR(32)=5, remainder 7
You can test it with:
FOR A%=1 to 65535:!in=A%:CALL sqr:P.A%,out?0,out?1:NEXT