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Since there are 3 digits in the given number, we set the indicator on
185 in the right-hand third of the K scale, and read the result 570 on
the D scale. We can place the decimal point by thinking of the nearest
perfect cube, which is 125. Therefore, the decimal point must be placed
so as to give 5.70, which is nearest to 5, the cube root of 125.

Example 42: cube_root( .034 ) = .324


Since there is one zero between the decimal point and the first digit
not zero, we must set the indicator over 34 on the middle third of the K
scale. We read the result 324 on the D scale. The decimal point may be
placed as follows:

cube_root( .034 ) = cube_root( 34/1000  )
                  = 1/10 cube_root( 34 )

The nearest perfect cube to 34 is 27, so our answer must be close to
one-tenth of the cube root of 27 or nearly 0.3. Therefore, we must place
the decimal point to give 0.324. A group of examples for practice in
extraction of cube root follows:

Example
43: cube_root( 64 ) = 4


44: cube_root( 8 ) = 2


45: cube_root( 343 ) = 7


46: cube_root( .000715 ) = .0894


47: cube_root( .00715 ) = .193


48: cube_root( .0715 ) = .415


49: cube_root( .516 ) = .803


50: cube_root( 27.8 ) = 3.03


51: cube_root( 5.49 ) = 1.76


52: cube_root( 87.1 ) = 4.43



THE 1.5 AND 2/3 POWER

If the indicator is set over a given number on the A scale, the number
under the hair-line on the K scale is the 1.5 power of the given
number. If the indicator is set over a given number on the K scale, the
number under the hair-line on the A scale is the 2/3 power of the given
number.

4 to the 3/2 power is 8
8 to the 2/3 power is 4.



COMBINATIONS OF PROCESSES

A slide rule is especially useful where some combination of processes is
necessary, like multiplying 3 numbers together and dividing by a third.
Operations of this sort may be performed in such a way that the final
answer is obtained immediately without finding intermediate results.