 | Charles Davies - Algebra - 1860 - 330 pages
...2a;y + y~ - &• + (2x + y)y. That is, the number is equal to the square of the tens in its roots, plus twice the. product of the tens by the units, plus the square of the units. EXAMPLE. 1. Extract the square root of 6084. Since this number is composed of more than two places... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...both members, N* = a? + 2ab '+ 62 : Hence, the square of a number is equal to the square of the lens, plus twice the product of the tens by the units, plus the square of the units. For example, 78 = 70 + 8, hence, (78)2 = (70)2 + 2 x 70 x 8 + (8)2 = 4900 + 1120 + 64 = 6084. 95* Let... | |
 | Charles Hutton - Mathematics - 1860 - 1020 pages
...second period 41, and annexing them on the right of 4, the result is 441, a number which contains tnice the product of the tens by the units, plus the square of the units. We may further prove, as in the last case, that if we point off the last figure 1, and divide the preceding... | |
 | Charles Davies - Algebra - 1861 - 322 pages
...Which proves that the square of a number composed of tens and units, equals the square of the lens plus twice the product of the tens by the units, plus the square of the units. 94. If now, we make the units 1, 2, 3, 4, &c., tens, or units of the second order, by annexing to each... | |
 | Education - 1861 - 552 pages
...period must be the square of the tens. After taking out this square of the tens, we have left the double product of the tens by the units plus the square of the units. By dividing the double product by double the tens, we find the units. BY inspection, we may often determine... | |
 | Thomas Sherwin - 1862 - 252 pages
...+ 9 = 529. Hence, When a number contains units and tens, its second power contains the second power of the tens, plus twice the product of the tens by the units, plus the second power of the units. Let us now, by a reverse operation, deduce the root from the power. Operation.... | |
 | Benjamin Greenleaf - 1863 - 338 pages
...square root. 2141 The square of any number, consisting of more than one place of figures, is equal to the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. For, if the tens of a number bo denoted by a, and the units by Ь, the number will be denoted by a... | |
 | Charles Davies - Arithmetic - 1863 - 346 pages
...33+ 2 (3 x 0) + 63: that is, 3 + 6 3 + 6 3x6 3' + 3 x 6 2(3x6) + 6 The square of a number is equal to the square of the tens plus twice the product of the tens by the units, plus th» square of the units. The same may be shown by the figure : Let the line AB represent the 3 tens... | |
 | Charles William Hackley - Algebra - 1864 - 532 pages
...2, or 3714 tens, plus two units.) ' Now the square of the root sought, that is, the proposed number, contains the square of the tens, plus twice the product of the tens by the units, pins the square of the units. But the square of the tens must give at least hundreds; hence the last... | |
 | Elias Loomis - Algebra - 1864 - 386 pages
...the number of tens, whose square is 400; and if we subtract this from 529, the remainder 129 contains twice the product of the tens by the units, plus the square of the units. If, then, we divide this remainder by twice the tens, we shall obtain the units, or possibly a number... | |
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Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units. 
