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. A Treatise on Algebra - Page 139by Elias Loomis - 1873 - 360 pagesFull view - About this book
| Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...it by adding it to the divisor : then multiplying the divisor thus completed by the units, we obtain **twice the product of the tens by the units, plus the square of the units.** Now if this quantity be greater than the tens of the dividend, the units in the root are too many,... | |
| Charles William Hackley - Algebra - 1846 - 544 pages
...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...tens by the units, plus the square of the units. But** the square of the tens must give at least hundreds ; hence the last two figures, 44, can form no part... | |
| Charles Davies - Arithmetic - 1846 - 378 pages
...square AE, the two rectangles FE and EC, and the square ED. Hence, The square of two 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.** Let it now be required to extract the square root of 1296. Since the number contains more than two... | |
| Charles William Hackley - Algebra - 1846 - 542 pages
...the second period 41, and annexing them on the right of 4, the result is 441, a number which contains **twice the product of the tens by the units, plus the square of the units.** We may farther prove, as ir the last case, that if we point off the last figure 1, and divide the preceding... | |
| Davis Wasgatt Clark - Algebra - 1846 - 374 pages
...Subtracting the square of this - - - 2116 Square of 4 tens, or 40 - - - - 1600 516 This remainder contains **twice the product of the tens by the units, plus the square of the units.** Now, if we double the tens, which gives 80, and divide 516 by 80, the quotient is the figure of the... | |
| Charles Davies - Arithmetic - 1847 - 368 pages
...square AE, the two rectangles FE and EC, and the square ED. Hence, The square of two 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.** Let it now be required to extract the square root of 1296. Since the number contains more than two... | |
| Charles William Hackley - Algebra - 1847 - 546 pages
...118'4 0. which sh*>ws thnt the square of a number consisting of (ens and units is composed of tliK **square of the. tens, plus twice the product of the tens by the units,** j)lus tlic square of the units. This being premised, since the square of a certain number of tens must... | |
| James Robinson (of Boston.) - 1847 - 304 pages
...figure, express tens ; hence, we infer that the second power of every number composed of tens and units **must contain the square of the tens, plus twice the product of the tens** multiplied by the units, plus the square of the units. We will now reverse the process of finding the... | |
| Charles Davies - Algebra - 1848 - 302 pages
...and (a+4)2=(64)2; or 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.** 94. If, now, we make the units 1, 2, 3, 4, &c, tens, or units of the second order, by annexing to each... | |
| Pliny Earle Chase - Arithmetic - 1848 - 244 pages
...the 7 in the root, and also at the right of the divisor, we multiply by 7, and obtain 469, which is **twice the product of the tens by the units plus the square of the units.** Hence we deduce the following RULE. *• Separate the number into periods of two figures each, by placing... | |
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