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" 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. tens? "
A Complete Arithmetic: Uniting Mental and Written Exercises in a Natural ... - Σελίδα 253
των Emerson Elbridge White - 1870 - 340 σελίδες
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The Normal Higher Arithmetic: Designed for Common Schools, High Schools ...

Edward Brooks - 1877 - 542 σελίδες
...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...

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

Stoddard A. Felter, Samuel Ashbel Farrand - 1877 - 471 σελίδες
...«'- : 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 - 1877 - 341 σελίδες
...method of finding the cube root of a number depends on the following principle of algebra: The cube of a number composed of tens and units is equal to the cube of the tens, plus three times the product of the squares of the tens by the units, plus three...

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

Benjamin Greenleaf - 1878 - 450 σελίδες
...hundreds, &c. of the square root of the number. 2. The square of a number consisting O/"TENS and UNITS if. equal to the square of the tens, plus twice the product of the tens into the units, plus the square of the units. Thus, if the tens of a number be denoted by a and the...

A Mental Arithmetic on the Inductive Plan: Being an Advanced Intellectual ...

Benjamin Greenleaf - 1879 - 180 σελίδες
...What is the 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...the tens by the units, plus the square of the units. Thus, 32 is 3 tens and 2 units ; 3 tens, or 30, squared is 900 : twice 30 by 2 units is 120; the square...

New Elementary Algebra: Designed for the Use of High Schools and ..., Βιβλίο 1

Benjamin Greenleaf - 1879 - 336 σελίδες
...figures in the square root. 211, The square of any number, consisting of more than one place of figures, is equal to the square of the tens, plus twice the...the tens by the units, plus the square of the units. For, if the tens of a number be denoted by a, and the units by b, the number will be denoted by a -f-...

Bradbury's Eaton's Practical Arithmetic: Combining Oral and Written Exercises

William Frothingham Bradbury - 1879 - 374 σελίδες
...From this example it can be seen that the square of a numbeï whose figures are tens and units equals The square of the tens plus twice the product of the tens by the units plus the square of the units. 86. Find the square root of 576. OPERATION. As 576 consists of three figures, its 576 (24 Aus square...

A Treatise on Algebra

Elias Loomis - 1879 - 384 σελίδες
...841 " 800+40+1. If, then, 841 is the square of a number composed of tens and units, it must contain the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. But these three terms are blended together in 841, and hence arises the peculiar difficulty in determining...

Bradbury's Eaton's Practical Arithmetic ...

William Frothingham Bradbury - 1882 - 374 σελίδες
...tens figure ' of the root must be 2. Now, as the number 576 equals the square of the tens of the root, plus twice the product of the tens by the units plus the square of the units, if we subtract from 576 the square of the tens of the root, that is 202, or 400, the remainder, 176,...

Ray's New Higher Arithmetic: A Revised Edition of the Higher Arithmetic

Joseph Ray - 1880 - 408 σελίδες
...as we treated the 2 tens in the first illustration. SECOND EXPLANATION. We learned in Art. 371 that the square of a number composed of tens and units...the tens by the units, plus the square of the units. The square of (20 + 4), or 242, is 202 + 2 X (20 X 4) + 42. Now, if the square of the tens be taken...




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