...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...

...figures, 84. The result of this operation, 1184, contains twice the product of the tens by the units, plue the square of the units. But since tens multiplied by units cannot give a product of a less unit than tens, it follows that the last figure, 4, can form no part of the double product of the tens...

...of 11, 0 to which we bring down the two | next figures 84. The result of this operation is 1184, mid this number is made up of twice the product of the...tens multiplied by units cannot give a product of a lower order than tens, it follows that the last number 4 can form no part of double the product of...

...of 11, 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...multiplied by units cannot give a product of a less unit than tens, it follows that the last figure, 4, can form no part of the double product of the tens...

...members, N2 = a* + 2ab + b2 : Hence, 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. For example, 78 = 70 + 8, hence, (78)2 = (70)2 + 2 X 70 X 8 + (8)2 = 4900 + 1120 + 64 = 6084. 95 1...

...+ 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...

...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...

...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...

...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...

...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...