Mathematics for Carpenters and Builders - Carpenter's and Builder's Math, Plans, and Specifications - page 131

2. Find the greatest cube that can be divided into the left-hand
group, and write its root for the first figure of the required
root.
3. Cube this root, subtract the result from the left-hand group,
and annex the next group to the remainder for a dividend.
4. For a partial divisor, take three times the square of the root
already found, considered as hundreds, and divide the dividend
by it. The quotient (or the quotient diminished ) will be (or be
close to) the second figure of the root.
5. To this partial divisor , add three times the product of the first
figure of the root, considered as tens, by the second figure, and
to this add the square of the second figure. This sum will be
the complete divisor .
6. Multiply the complete divisor by the second figure of the root,
subtract the product from the dividend, and annex the next
group to the remainder for a new dividend.
7. Proceed in this manner until all the groups have been annexed.
The result will be the cube root required, as shown in the
following example.

Example The problem: Extract the cube root of the number 50,653.
The solution:

√ 50 653

3

. ( 37

27

2700 23 653

630 23 653

49
3379

Therefore, the cube root of 50,653 is 37.

Measures
To measure is the act or process of determining the extent, quantity,
degree, capacity, dimension, volume, and so forth, of a substance
by comparing it with some fixed standard, which is usually fixed
by law. A measure may relate to any of these standards. There are
many kinds of measures, and practically all of them are standard,
but standards vary in different countries. The measures mentioned
in this text are all U.S. standards unless designated otherwise. The
study of measurements is sometimes called mensuration .