...(60)2 + 2 X 60 X 4 + (4)2 = 4096. Hence, 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. 117. If now, we make the units 1, 2, 3, 4, &c., tens, by annexing to each a cipher, we shall have,...

...it by adding it to the divisor : then multiplying the divisor thus completed by the units, we obtain twice the product of the tens by the units, plus the square of the units. Now if this quantity be greater than the tens of the dividend, the units in the root are too many,...

...of the square AE, the two rectangles FE and EC, and the square ED. Hence, The square of two figures is equal to the square of the tens, plus twice the...the tens by the units, plus the square of the units. Let it now be required to extract the square root of 1296. Since the number contains more than two...

...3714 tens, plus two units.) Now the square of the root sought, that is, the proposed number, contains the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. But the square of the tens must give at least hundreds ; hence the last two figures, 44, can form no...

...the 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 the units. We may farther prove, as ir the last case, that if we point off the last figure 1, and divide the preceding...

...of the square AE, the two rectangles FE and EC, and the square ED : Hence The square of two figures is equal to the square of the tens, plus twice the product of tlie tens Jy the units, plus the square of the units. Let it now be required to extract the square...

...+ 24000+3000+125 = 91125 283. On inspecting the above examples, it will be perceived that the cube of a number composed of tens and units is equal to the cube of the tens, plus three times the product of the square of the tens by the units, plus three times...

...of the square AE, the two rectangles FE and EC, and the square ED. Hence, The square of two figures is equal to the square of the tens, plus twice the...the tens by the units, plus the square of the units. Let it now be required to extract the square root of 1296. Since the number contains more than two...

...118'4 0. which sh*>ws thnt the square of a number consisting of (ens and units is composed of tliK square of the. tens, plus twice the product of the tens by the units, j)lus tlic square of the units. This being premised, since the square of a certain number of tens must...

...tens ; hence, we infer that the second power of every number composed of tens and units must contain the square of the tens, plus twice the product of the tens multiplied by the units, plus the square of the units. We will now reverse the process of finding the...