...400+280+49=729. 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...

...numbers of the orders of the root. 4. Every square consisting of mare than two orders of figures w equal to the square of the tens in its root, plus...the tens by the units, plus the square of the units. NOTE.— The square of a fraction cauuot be integral, or, which is the same thing, an integer cannot...

...number 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...

...further, that (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...

...square of 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,...

...hundreds' place, and subtract , this takes _ away the square of the tens, and leaves 3'JG, 66)396 which is twice the product of the tens by the units plus the square of the units. If now, we double the divisor and then divide this remainder, exclusive of the right hand figure, (since...

...tens and units. Let N denote such a number, x the tens of its square root, and y the units; then will that is, the number is equal to the square of the...of tens can contain no significant figure less than hundreds, the two figures on the right may be pointed off, and the square of the tens will be found...

...point. If we subtract the square of the tens from the given number, the remainder will be equal to twice the product of the tens by the units, plus the square of the units. Consequently, if we divide the remainder by twice the tens, the quotient will give the units, or a...

...of algebra : 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...

...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...