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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

## A Complete Arithmetic: Uniting Mental and Written Exercises in a Natural ...

Emerson Elbridge White - Arithmetic - 1870 - 348 pages
...shown that the square of any number, composed of tens and units, is equal to The square of the t&ns. plus twice the product of the tens by the units, plus the square of the units. 33. What is the square of 45? f402 =1600 PROCESS: 452 = ) = 400 ( 2025, Afts. 34. What is the square...

## School Arithmetic: Analytical and Practical

Charles Davies - Arithmetic - 1874 - 346 pages
...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...

## A Higher Arithmetic

George Payn Quackenbos - Arithmetic - 1874 - 444 pages
...ordinary way, we deduce the following law : — The square of a number composed of tens and units, equals the square of the tens, plus twice the product of the tens and units, plus the square of the units. The diagram in the margin will illustrate this law of numbers,...

## Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 pages
...root, and y the units; then will that is, the number is equal to the square of the tens in its root, plus twice the product of the tens by the units, plus the square of the units. We first find the tens of the root. Since the square of tens can contain no significant figure less...

## Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 pages
...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...

## A Mental Arithmetic on the Inductive Plan ...

Benjamin Greenleaf - 1875 - 196 pages
...square of 75 ? Of 85 ? 8. What is the square of 32 ? NOTE. — The square of any number is equal to the square of the tens, plus twice the product of the tens Ъу the units, plus the square of the units. Thus, 32 is 3 tens and 2 units ; 3 tens, or 30, squared...

## Complete Arithmetic: Comprising the New Intermediate Arithmetic and Part of ...

Stoddard A. Felter, Samuel Ashbel Farrand - Arithmetic - 1877 - 496 pages
...«'- : hence we have the following FORMULA. — The square of a number expressed by two figures equals the square of the tens, plus twice the product of...the tens by the units, plus the square of the units ; or, (t + «)2 = i2 + 2 tu + M2. WRITTEN EXEIiCISES. PROBLEM. — Write the square of 85. PKOCESS....

## Complete Arithmetic: Theoretical and Practical

William Guy Peck - Arithmetic - 1877 - 430 pages
...the following principle 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...

## The Normal Higher Arithmetic: Designed for Common Schools, High Schools ...

Edward Brooks - Arithmetic - 1877 - 528 pages
...OPERATION. 45 = 45 = 225 = 180 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...

## The New American Arithmetic, Part 3

Samuel Mecutchen, George Mornton Sayre - Arithmetic - 1877 - 200 pages
...units. This analysis indicates that the square of a number consisting 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. To prove the accuracy of the proposition, let the tens of a number be denoted by a, and the units by...