...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...

...= 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...

...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 unit than tens, it follows that...

...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...

...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...

...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 unit than tens, it follows that...

...is the square of 60, from the given number, we have the remainder 756, which must contain twice the product of the tens by the units, plus the square of the units, or 2 ab -|- b3. Dividing this remainder by 2 a, that is by 120, gives 6, which is the value of 6. Then...

...certain nuro her of units, tens, hundreds, &c. Thus, 529 is equivalent to 500+20+9. Also, 841 " 800+40+1. 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...

...the square of a number composed of tens and units consists of the square of the tens, plus twice the product of the tens by the units, plus the square of the units. If we reverse this process, we shall find the square root of the number. Thus we perceive that the...

...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. (Art. 395.) Hence, the difference between 3364 and the square of the 5 tens of its root, is composed...