(151): if there be ciphers at the beginning of the divisor, if it be, for example, ·3178 ·003178, since this is -----, 100 divide by ·3178 in the usual way, and afterwards multiply the quotient by 100, or remove the decimal point two places to the right. If, therefore, six decimals be required, eight places must be taken in dividing by ·3178, for an obvious reason. In finding the last figure of the quotient, the nearest should be taken, as in the second of the subjoined examples. Places required, 2 8 Divisor, ·41432 3·1415927 Dividend, 673·1489 2·71828180 41432 2·51327416 -------- ---------- 258828 20500764 248592 18849556 ------- -------- 10237[21] 1651208 8286 1570796 ----- ------- 1951 80412 1657 62832 ----- ----- 294 17580 290 15708 --- ----- 4 1872 4 1571 - ---- 0 301 283 --- 18 19 -- Quotient, 1624·71 ·86525596 [21] This is written 7 instead of 6, because the figure which is abandoned in the dividend is 9 (151). Examples may be obtained from (143) and (150). SECTION VII. ON THE EXTRACTION OF THE SQUARE ROOT. 156. We have already remarked (66), that a number multiplied by itself produces what is called the _square_ of that number. Thus, 169, or 13 × 13, is the square of 13. Conversely, 13 is called the _square root_ of 169, and 5 is the square root of 25; and any number is the square root of another, which when multiplied by itself will produce that other. The square root is signified by the sign _ √ or √ ; _______ thus, √25 means the square root of 25, or 5; √(16 + 9) means the square root of 16 + 9, and is 5, and must not be confounded with √16 + √9, which is 4 + 3, or 7. 157. The following equations are evident from the definition: