 | 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... | |
 | Charles Davies - Arithmetic - 1848 - 372 pages
...rectangles FE and EC, and the square ED. Hence, 30 The square of two figures is equal to the square of ths tens, plus twice the product of the tens by the units, plus tht square of the units. Let it now be required to extract the square root of 1296. Since the number... | |
 | Charles Davies - Arithmetic - 1850 - 412 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 Davies - Algebra - 1850 - 292 pages
...1 , 0~ to which we bring down the two next figures 84. The result of this operation, 1184, contains twice the product of the tens by the units, plus the square of the units. But since tens multiplied by units cannot give a product, of a less name than tens, it follows that... | |
 | Charles Davies - 1852 - 344 pages
...sum is 32+2(3 x 6)+62 : that is, 3 + 6 3 + 6 32+3x6 3'+2(3x6)+6 H The square of a number is equal to the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. The same may be shown by the figure : Let the line AB re- F 30 IP present the 3 tens or 30, and BC... | |
 | Dana Pond Colburn - Arithmetic - 1852 - 228 pages
...the same units' figure, must equal the product of the tens by the tens, plus the product of the sum of the tens by the units, plus the square of the units. Show the truth of the following equations : — 67 times 37 = 60 times 30 -f- 7 times 90 + 7 times... | |
 | David Henry Cruttenden - Arithmetic - 1853 - 330 pages
...square of 45. Thus, 45 = 40+ 5 40+ 5 200 + 25 1600 + 200 Hence, 452 = 1600+400 +25=2025 Ans. That is, the square of the tens, plus twice the product of the tens into the units, plus the square of the units. 16. What is the 4th power of 12 ? Ans. 20,736. 17. Find... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...841 " 800+40 + 1. If, then, 841 is the square of a number composed of tens and units, it must contain the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. But these three terms are blended together in 841, and hence the peculiar difficulty in determining... | |
 | Thomas Sherwin - Algebra - 1855 - 262 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.... | |
 | William Smyth - Algebra - 1855 - 370 pages
...= 2209. Thus the square of a number, consisting of units and tens, is composed of three parts, viz. the square of the tens, plus twice the product of the tens multiplied by the units, plus the square of the units. Thus in 2209, the square of 47, we have The... | |
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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. 
