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233. Corollary. If the given equation is a binomial one, as in art. 149, we can obtain, by this process, a root of any degree whatever.

EXAMPLES.

1. Extract the square root of 5 by means of continued fractions.

Solution. Representing this root by x, we have

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which, being precisely the same with the equation for x', we may conclude that

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2. Extract the third root of 46 by means of continued

fractions.

Ans. 3,583.

3. Extract the third root of 35 by means of continued

fractions.

Ans. 3,271.

4. Extract the square root of 2 by means of continued fractions.

22

Ans. 1,4142136.

1

EXPONENTIAL EQUATIONS

AND

LOGARITHMS.

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