...double the tens plus the units, or 2 a + b ; this multiplied by 7 or b, reproduces 609 = 2a6 + 6s, or double the product of the tens by the units, plus...subtracted leaves no remainder, and the operation •hows, that 47 is the square root of 2209. If it were required to extract the square root of 324...

...double the tens plus the units, or 2 a -f- 6 ; this multiplied by 7 or 6, reproduces 609 = 2a b -\- b3, or double the product of the tens by the units,...root of 324; the operation would be as follows ; 3,24 18 1 22,4 2& 224 Proceeding as in the last example, we obtain 1 for the place of tens of the root;...

...for the square, the number 2916, which, as we see, is composed of the square of the tens, plus twice the product of the tens by the units, plus the square of the units of the number 54. 134. What we have, observed being an immediate consequence of the rules of multiplication,...

...the square of a number consisting of tens and units is made up of the square of the units, plus twice the product of the tens, by the units, plus the square of the tens. See this exhibited in figure F. As 10X 10=100, the square of the tens can never make a part of...

...the square of a number consisting of tens and units is made up of the square of the units, plus twice the product of the tens, by the units, plus the square of the tens. See this exhibited in figure F. As 10X 10=100, the square of the tens cau never make a part of...

...that 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 figure a cipher, we shall...

...units, we shall have, for the square of a + b, a2 + 2ab + b ; that is, the square of the tens, twice the product of the tens by the units, plus the square of the units. Let a = 8, and b — then, since a represents the tens, and b the units, a + b becomes 80 + 5 = 85...

...have, for a remainder, after the the square of the tens is taken out, 825. This must contain the double product of the tens by the units, plus the square of the units. If we could separate the square of the units from the double product in this number, we should, evidently,...

...to which we 0 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 name than tens, it follows that...

...that 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. 94. If, now, we make the units 1,2, 3, 4, &c, tens, or units of the second 'order, by annexing to each...