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This section deals with the expressions involving squares and square roots. At one level they can be treated as a purely mechanical exercise - a detailed list of slide and cursor movements. However they can also be considered as way of understanding more completely the scales on a rule.
I suggest that rather then move your rule following the instructions, and realiisng that they do work as intended, you should hide the "method" column and try to work out for yourself what movements are appropriate. The basic concept is quite simple. Any calculations involving squares start on the C and D scales and end up on the A and B scales and any calculations involving square roots start on the A and B scales and end up on the C and D scales. When you have worked through the examples in the table you should find it each to deal with...
6.32 x Ö(7.28 x 4.12 / (8.05 x 12.1))
...you calculate everything to the right of the square root sign using the A and B scales, transfer the answer to the D scale and multiply by 6.32 using the C scale.
Similarly to calculate ...
6.32 x (7.28 x 4.12 / (8.05 x 12.1))2
... you calculate everything to be squared on the C and D scales, transfer the answer to the A scales and multiply by 6.32 on the B scale.
The table below is based on instructions from The Slide Rule - a Practical Manual by C. N. Pickworth.
| Equation | Method |
| a x b2 | Set the index of C to b on D, and over a on B read answer on A. |
| a2 / b | Set b on B to a on D by using the cursor, and over index of B read answer on A. |
| b / a2 | Set a on C to b on A, and over 1 on B read answer on A. |
| a x b2 / c | Set c on B to b on D, and over a on B read answer on A. |
| (a x b)2 | Set 1 on C to a on D, and over b on C read answer on A. |
| (a / b )2 | Set b on C to a on D, and over 1 on C read answer on A |
| Ö (a x b) | Set 1 on B to a on A, and under b on B read answer on D. |
| Ö (a / b) | Set b on B on a on A, and under 1 on C read answer on D. |
| a x b / c2 | Set c on C to b on A and over a on B read answer on A. |
| c Ö (a / b) | Set b on B to a on A, and under c on C read answer on D. |
| (Ö a) / b | Set b on C to a on A, and under 1 on C read answer on D. |
| a / (Ö b) | Set b on B to a on D, and under 1 on C read answer on D. |
| b x (Ö a) | Set 1 on C to b on D, and under a on B read answer on D. |
| Ö (a x b / c) | Setcon B to a on A, and under b on B read answer on D. |
| (a x b) /(Ö c) | Set c on B to b on D, and under a on C read answer on D. |
| Ö (a2 x b / c) | Set c on B to a on D, and under b on B read answer on D. |
| a2 x b2 / c | Set c on B to a on D, and over b on C read answer on A. |
| a x (Ö b) / c | Set c on C to b on A, and under a on C read answer on D. |
| ( x (Ö b) / c)2 | Set c on C to a on D, and over b on B read answer on A. |