...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 tin- units. W^e may farther prove, as in the last case, that if we point off the last figure 1, and...

...Hence 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...

...root. 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...

...consisting of tens and units. The square of such a number is equal to the Bquare of the tens, plus twice the product of the tens by the units, plus the square of the units. Thus 25 is composed of 2 tens or 20 and 5 units; and the 20 squared equals, 4:00 20 multiplied by 5...

...(he square of any number separated into 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. 355, 1.) :>('>,'>. These two principles concerning the number of orders in any square, and the...

...any number expressed by more than one order of figures consists of the square of the tens, plus twice the product of the tens by the units, plus the square of the units. For any number expressed by more than one order of figures may be regarded as an algebraic polynomial,...

...2xy + f = а? + (2ж that is, the number is equal to the square of the tens in its root, plus twice the product of the tens by the units, plus the square of the units. We first find the tens of the root. Since the square of tens can contain no significant figure less...

...: 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. ROOTS. This may be illustrated geometrically. For, let A be a square, each of whose sides is equal...

...root. (3.) The square of the tens taken from the power leaves a remainder of 625, which contains twice the product of the tens by the units, plus the square of the units. (4.) Twice 6 tens are 12 tens, or 120, and 120 is contained 5 times in 625: 5 is therefore probably...

...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...