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Which proves 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.
A Treatise on Algebra - Page 139
by Elias Loomis - 1873 - 360 pages

## An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...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,...

## A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 544 pages
...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...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 part...

## The University Arithmetic: Embracing the Science of Numbers, and Their ...

Charles Davies - Arithmetic - 1846 - 378 pages
...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...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...

## A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 pages
...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...

## Elements of Algebra: Embracing Also the Theory and Application of Logarithms ...

Davis Wasgatt Clark - Algebra - 1846 - 374 pages
...Subtracting the square of this - - - 2116 Square of 4 tens, or 40 - - - - 1600 516 This remainder contains twice the product of the tens by the units, plus the square of the units. Now, if we double the tens, which gives 80, and divide 516 by 80, the quotient is the figure of the...

## Arithmetic: Designed for Academies and Schools, Uniting the Inductive ...

Charles Davies - Arithmetic - 1847 - 368 pages
...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...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...

## A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1847 - 546 pages
...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...

## The American Arithmetic

James Robinson (of Boston.) - 1847 - 304 pages
...figure, express 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...