Cube Roots of Compound Expressions.

This trial divisor is $86, 700$ , and if we add $3 a b + b^{2}$ to complete the divisor, when $b = 1$ , the complete divisor will be $86, 700 + 511 = 87, 211$ , and this is larger than the dividend $87, 000$ . We therefore put $0$ for the next figure of the root. We then bring down another group and annex two more ciphers to the trial-divisor.

The last two figures of the root are found by division. The rule in such cases is, that two less than the number of figures already obtained may be found without error by division, the divisor being three times the square of the part of the root already found.

The cube root of a common fraction whose denominator is not a perfect cube can be found approximately by reducing the fraction to a decimal, and then extracting the root.

Exercise 81.

Find the cube root of:

$46, 656$ .

$42, 875$ .

$91, 125$ .

$274, 625$ .

$110, 592$ .

$258, 474, 853$ .

$109, 215, 352$ .

$259, 694, 072$ .

$127, 263, 527$ .

$385, 828, 352$ .

$1879.080904$ .

$1838.265625$ .

Find to four decimal places the cube root of:

$0.01$ .

$0.05$ .

$0.2$ .

$4$ .

$10$ .

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