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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

## The Elements of Algebra

Elias Loomis - Algebra - 1856 - 280 pages
...whose square is a'+2ab+b'. Hence we see 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. Now the square of tens can give no significant figure in the first right-hand period ; the square of...

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

Charles Davies - Arithmetic - 1856 - 450 pages
...When «o, decomposed, what IN its square equal to ' F 30 30 The square of a number is equal to ike 'square of the tens, plus twice the product of the tens by the units, plus the square of the units. The same may be shown by a figure : Let the line AB represent the 3 tens or 30, and BC the six units....

## The Intellectual Multiplier: Comprising Concise and Easy Methods of ...

Arithmetic - 1856 - 46 pages
...itself is called the square, or second power, of that number. The square of any number is equal to the square of the tens, plus twice the product of the tens multiplied by the units, plus the square of the units. 1. What is the product of 125 multiplied by...

## The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1857 - 452 pages
...number of periods 66396 is two, the root will consist of two figures, 396 tens and units. Then 1296 = the square of - the tens plus twice the product of the tens 0 into the units, plus the square of the units. The square of tens is hundreds, and must therefore...

## The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1858 - 458 pages
...periods C 6 3 9 6 is two, the root will consist of two figures, 3 9 (J tens and units. Then 1296 = the square of the tens plus twice the product of the tens 0 into the units, plus the square of the units. The square of tens is hundreds, and must therefore...

## A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - Algebra - 1858 - 344 pages
...= 2209. Thus the square of a number, consisting of units and tens, is composed of three parts, viz. the square of the tens, plus twice the product of the tens multiplied by the units, plus the square of the units. Thus in 2209, the square of 47, we have The...

## The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1858 - 456 pages
...of periods 66396 is two, the root will consist of two figures, 3 g (] tens and u»it.t. Then 1296 = the square of the tens plus twice the product of the tens 0 into the unit;!, plus the square of the units. The square of tens is hundreds, and must therefore...

## Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 412 pages
...b; whence, by squaring both members, N2 = a* + 2ab + b2 : Hence, the square of a number is equal to the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. For example, 78 = 70 + 8, hence, (78)2 = (70)2 + 2 X 70 X 8 + (8)2 = 4900 + 1120 + 64 = 6084. 95 1...