TABLES OF ROOTS
The decimal values of square roots and cube roots
of numbers with as many as 3 or 4 digits can
be found from tables. The table in appendix I of this course gives the square
roots and cube roots of numbers from 1 to
100. Most of the values given in such tables
are approximate numbers which have been
rounded off. For example the fourth column in
appendix I shows that
= 8.4853, to 4 decimal places. By shifting
the decimal point we can obtain other square
roots. A shift of two places in the decimal
point in the radicand corresponds to a shift
of one place in the same direction in the square
root.
The following examples show the effect, as reflected
in the square root, of shifting the location
of the decimal point in the number whose
square root we seek:
Cube Root
The fifth column in appendix I shows that the cube
root of 72 is 4.1602. By shifting the decimal point we immediately have the cube
roots of certain other numbers involving the
same digits. A shift of three places in the
decimal point in the radicand corresponds to
a shift of one place in the same direction in
the cube root.
Compare the following examples:
Many irrational numbers in their simplified forms
involve and
Since these radicals occur often, it is
convenient to remember their decimal
equivalents as follows:
Thus any irrational numbers that do not contain any
radicals other than or
can be converted to decimal forms quickly without referring to tables.
For example consider
Keep in mind that the decimal equivalents of
and as used in the foregoing examples are
not exact numbers and the results obtained with
them are approximate in the fourth decimal place.
