Odd Sub-Products

Given problem

√28,679,87

*Left C, 1st R (left column, first row)

√28’67’98’76
5 M N 4
5 M N 6

*Right C, 1st R

P Chk

… Let P = 28’67…
…......... . . . = . . .
…4↓ / 55..2 = 30’25.. \ P
.……\ 50..2 = 25’00.. /
M = 4, 3, 2, 1, 0

*Left C, 2nd R

5MN42 = ..16
..Nx4x2 = ..6 .
………… ..76
Nx8 = ..6 …. N = 2, 7
4M24

4M74

*Right C, 2nd R

5MN62 = ..36
..Nx6x2 = ..4 .
………… ..76
Nx2 = ..4 …. N = 2, 7

4M26

4M76

*Left C, 3rd R

5M242 = ..04’16
....2x4x2 = ..1’6 .
.……….. ..05’76
.Mx4x2 = .. 3 .
.………… ..8’76

5M24 ≠ √P

*Right C, 3rd R

5M262 = ..04’36
...2x6x2 = .. 2’4 .
.……….. ..06’76
..Mx6x2 = ..2 ....
.………… ..8’76
Mx2 = ..2 … M = 1, 6

5126

*Left C, 4th R

5M742 = ..49’16
....7x4x2 = ..5’6 .
.……….. ..54’76
..Mx4x2 = ..4 .
………… ..8’76
Mx8 = ..4 … M = 3, 8
5374

*Right C, 4th R

5M76 ≠ √P

*Left C, 5th R

Sq. Rt. Loc 1

↓5126 … 5374↑
… / H = 30’25.. \
. ↑ \ M = 27’56.. / P
…... L = 25’00..
……….. 55’25 / 2
……….. 27’62 – 6 = 27’56


*Right C, 5th R

√28’67’98’76 = 5,374


There are cases that the sub-products end with an ‘odd numbers’. If you look at the equation at left C, 3rd R, the last product should supposed to end with 3. But as a general rule in SSQ, “the product of a sub-product must always be in even number.”

The reason why I gave an advice, to separate your paper into two columns, is for you to make it ‘easier’ to see the patterns of each equation.

1) If the left C, 3rd R is not a square root of P (≠ √P), it follows then, that the right C, 4th R is automatically not a square root of P and vice versa.

2) If the right C, 3rd R is not a square root of P (≠ √P), it follows then, that the left C, 4th R is automatically not a square root of P and vice versa.

3) It is easier to arrange the possible square roots from lowest to highest because there is always a pattern. See it to yourself