...the number of tens, whose square is 400; and if we subtract this from 529, the remainder 129 contains twice the product of the tens by the units, plus the square of the units. If, then, we divide this remainder by twice the tens, we shall obtain the units, or possibly a number...

...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 the tens by the units, pins the square of the units. But the square of the tens must give at least hundreds; hence the last...

...period, and subtract; this 85^42 5 takes away the square of the tens, and leaves 42 5 425, which is twice the product of the tens by the units plus the square of the units. If, now, we double the tens, and then divide the remainder, exclusive of the right-hand figure (since...

...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 ly the units, plus the square of the units. But these three terms are blended together in 841, and...

...6) + 63 : that is, Rule. — The square of a number is equal to the square of the tens, plus turice the product of the tens by the units, plus the square of the units. 379. To find the square root of any number. 1. Let it now be required to extract the square root of...

...1. What is the square of a quantity ? Art. 93. 2. Define the Square Root of a quantity. Art. 93. 3. The square of a Number composed of tens and units is equal to what? Art. 94. 4. Illustrate the last question by squaring 64. 5. Also by squaring 365. 6. Extract...

...1. What is the square of a quantity? Art. 93. 2. Define the Square Root of a quantity. Art. 93. 3. The square of a Number composed of tens and units is equal to what? Art. 94. 4. Illustrate the last question by squaring 64. 5. Also by squaring 365. 6. Extract...

...or a2+2a6 + b-= 400+280+49=729. Hence the square of a number composed of tens and units consists of the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. If we reverse this process, we shall find the square root of the number. Thus we perceive that the...

...certain number of units, the 782 725 5714 4509 12054 4 12054 4 given number will, as before, be 150 3 equal to the square of the tens plus twice the product of the tens by 1506 8 the units plus the square of the units. If then, as before, we point off it period of two figures,...

...is the square of 75 ? Of 85 ? 8. What is the square of 32 ? NOTE. — The square of any number ¡я equal to the square of the tens, plus twice the product...the tens by the units, plus the square of the units. Thus, 82 is 3 tens and 2 units ; 3 tens, or 30, squared is 900 : twice 30 by 2 units is 120; the square...