As the extraction of the square-root of numbers is required to calculate the strength of timber, the rule will be given below, more to refresh the memory than to give original information as to its principles; it being presumed that every intelligent workman has made himself familiar with the rules of common arithmetic through works especially designed for the purpose.

Rule. - 1st, Separate the given number into periods of two figures each, by placing a point over the first figure at the right hand, and then over every other figure towards the left.

2d, Ascertain the greatest square-number contained in the left-hand period, and place the root of it at the right hand of the given number, after the manner of a quotient in division. Subtract the square of this root from the period named, and to the remainder bring down the next period for a new dividend.

3d, Double the quotient already found, and place it at the left of the dividend for a divisor. Find how many times this divisor is contained in the new dividend {omitting the right-hand figure), and place the Jigure in the root as the second figure of the same, and likewise on the right hand of the divisor. Multiply the divisor by the last quotient-figure, subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

4th, Double the quotient already found for a partial divisor, and from these find the next figure in the root as before directed: so continue the operation until all the periods have been employed. Should a remainder exist, add two ciphers as a new period, and so continue pointing off the root after the rules of decimal fractions.

Example. - What is the square-root of 59,325 ?

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59325 (243.5 4

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44)193 176

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483) 1725 1449

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4865) 27600 24325

Required the square-root of 326,041: 326041(571 25

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107) 760 749

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