Mathematics for Carpenters and Builders - Carpenter's and Builder's Math, Plans, and Specifications - page 130

is produced. This number is indicated by the symbol √ , called the
radical sign , which, when placed over a number, means that the root
of that number is to be extracted. Thus:
√ 4 means that the square root of 4 is to be extracted
The index of the root is a small figure that is place d over the
radical sign that denotes w ha t root is to be taken. Thus,

√ 9 indicates

3

√ 16 indicates the extraction of the fourth
root of 16. When there is no index given, the radical sign alone
always means the square root is to be extracted from the number
under the radical sign.
Sometimes the number under the radical sign is to be raised to a
power before extracting the root, as follows:

4

the cube root of 9 and

√ 64
Example The problem: Extract the square root of 186,624.
The solution:
√ 18 66 24

√ 4 3 4

3 3

3

= × 4 × 4 =

432

16

83 √ 266
249

862 √ 1724
1724
From the decimal point, count off the given number into periods
of two places each. Begin with the last period counted off (18). The
largest square that can be divided into 18 is 4. Put this down in
the quotient, and put the square (16) under the 18. Write down
the remainder (2), and bring down the next period (66). Multiply
4 (in the quotient) by 2 for the first number of the next divisor;
8 goes into 26 three times. Place 3 after 4 in the quotient and also
after 8 in the divisor. Multiply the 83 by 3, placing the product 249
under 266, and subtract, obtaining the remainder 17. Bring down
the last period (24), and proceed as before, obtaining 432 as the
square root of 186,624.
Extracting the cube root of a number is a more compli-
cated (though similar) process, as indicated by the following
procedure:
1. Separate the number into groups of three figures each, begin-
ning at the decimal point.