 | Edward Brooks - Arithmetic - 1877 - 528 pages
...OPERATION. 45 = 45 = 225 = 180 40+5 40+5 40X5+52 = 40*+40X5 2025 = 402+2(40x5)+5a FQ the square of 45 equals the square of the tens, plus twice the product of...the tens by the units, plus the square of the units, which we find to be 2025. SYNTHETIC SOLUTION. — Let the line AB represent a length of 40 units, and... | |
 | Samuel Mecutchen, George Mornton Sayre - Arithmetic - 1877 - 200 pages
...units. This analysis indicates that the square of a number consisting of tens and units is equal to the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. To prove the accuracy of the proposition, let the tens of a number be denoted by a, and the units by... | |
 | William Frothingham Bradbury - Arithmetic - 1879 - 392 pages
...From this example it can be seen that the square of a numbeï whose figures are tens and units equals The square of the tens plus twice the product of the tens by the units plus the square of the units. 86. Find the square root of 576. OPERATION. As 576 consists of three figures, its 576 (24 Aus square... | |
 | Elias Loomis - Algebra - 1879 - 398 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 arises the peculiar difficulty in determining... | |
 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...squave root. 214, 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 be denoted by а, and the units by b, the number will be denoted by a... | |
 | Benjamin Greenleaf - Arithmetic - 1879 - 190 pages
...square of 75 ? Of 85 ? 8. What is the square of 32 ? NOTE. — The square of any 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. Thus, 32 is 3 tens and 2 units ; 3 tens, or 30, squared is 900 : twice 30 by 2 units is 120; the square... | |
 | William Frothingham Bradbury - 1882 - 416 pages
...tens figure ' of the root must be 2. Now, as the number 576 equals the square of the tens of the root, plus twice the product of the tens by the units plus the square of the units, if we subtract from 576 the square of the tens of the root, that is 202, or 400, the remainder, 176,... | |
 | Joseph Ray - Arithmetic - 1880 - 420 pages
...EXPLANATION. We learned in Art. 371 that the square of a number composed of tens and units 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 square of (20 + 4), or 242, is 202 + 2 X (20 X 4) + 42. Now, if the square of the tens be taken... | |
 | George E. Seymour - Arithmetic - 1880 - 332 pages
...+ 2 (20X5) + (5)! 487. Hence, The square of any number consisting of tens and units is composed of the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. 488. From this general law it follows a. That if from the square of a number, the square of the tens... | |
 | H. Bryant - 1881 - 574 pages
...used. 304. Observe further, that the square af any number separated into tens and units is equal to the square of the tens, plus twice the product of the tens by (he units, plus the square, of the units. (Art. 355, 1.) 36'J. These two principles concerning 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. 
