I have been assigned to find out how a calculator figures out square roots, so far the shortest thing I can see is "the duplex method". But the thing is that the explanation on Wikipedia makes no sense for me:
"
Find the square root of 2,080,180,881. Solution by the duplex method: this ten-digit square has five digit-pairs, so it will have a five-digit square root. The first digit-pair is 20. Put the colon to the right. The nearest square below 20 is 16, whose root is 4, the first root digit. So, use 2·4=8 for the divisor. Now proceed with the duplex division, one digit column at a time. Prefix the remainder to the next dividend digit.
divisor; gross dividend: 8) 20: 8 0 1 8 0 8 8 1 read the dividend diagonally up: 4 8 7 11 10 10 0 8 minus the duplex: 16: xx 25 60 36 90 108 00 81 actual dividend: : 48 55 11 82 10 00 08 00 minus the product: : 40 48 00 72 00 00 0 00 remainder: 4: 8 7 11 10 10 0 8 00 quotient: 4: 5, 6 0 9. 0 0 0 0 Duplex calculations: Quotient-digits ==> Duplex deduction. 5 ==> 52= 25 5 and 6 ==> 2(5·6) = 60 5,6,0 ==> 2(5·0)+62 = 36 5,6,0,9 ==> 2(5·9)+2(6·0) = 90 5,6,0,9,0 ==> 2(5·0)+2(6·9)+ 0 = 108 5,6,0,9,0,0 ==> 2(5·0)+2(6·0)+2(0·9) = 0 5,6,0,9,0,0,0 ==> 2(5·0)+2(6·0)+2(0·0)+92 = 81
Hence the square root of 2,080,180,881 is exactly 45,609.
" What does it actually mean by dividend diagonally up, where do the rows connect, how does the answer come out to 45609?
Please help me understand, sorry if this seams like a pointless question but it's my first time here.