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 139by Elias Loomis - 1873 - 360 pagesFull view - About this book
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
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