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Bøker Bok 110 av 15... brought down, there is no remainder, the proposed number is a perfect square....
" ... brought down, there is no remainder, the proposed number is a perfect square. But if there is a remainder, you have only found the root of the greatest perfect square contained in the given number, or the entire part of the root sought. For example,... "
Elements of algebra - Side 116
av Bourdon (Louis Pierre Marie, M.) - 1838 - 355 sider
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Elements of Algebra: Tr. from the French of M.Bourdon. Revised and Adapted ...

Charles Davies - 1835 - 353 sider
...entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root...of 25 the greatest perfect square contained in 665 1 that is, is 25 the entire part of the root ? To prove this, we will first show that, the difference...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1839 - 252 sider
...if it were required to extract the square root of 665, we should find 25 for the entire part of llic root, and a remainder of 40, which shows that 665 is not a perfect square. Bufis the square of 25 the greatest perfect square contained in 665 ? that is, is 25 the entire part...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1841 - 252 sider
...entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root,...in 665 ? that is, is 25 the entire part of the root 1 To prove this, we will first show that, the difference between the squares of two consecutive numbers,...
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Elements of Arithmetic and Algebra: For the Use of the Royal Military College

William Scott - 1844 - 500 sider
...numbers ; then (a+l)!=(a+l) (a+l)=as+2a+l (Art. 76), and a*=aXa=a! ; .-.(a+1)2— a"=2a+l. ' Whence the difference between the squares of two consecutive numbers is equal to twice the less number + 1 ; the greater, therefore, the number a the greater is the difference between (<z+l)2 and a2, and...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1848
...entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root,...in 665 ? that is, is 25 the entire part of the root 1 To prove this, we will first show that, the difference between the squares of two consecutive numbers,...
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A New System of Arithmetic on an Improved Plan

Charles Guilford Burnham - 1850
...contained in 572 ; that _^ is, it is the entire part of the root. This . , • „„ may be shown, thus : The difference between ' the squares of two consecutive numbers, is equal to twice the less number, plus 1 . The 43 dift'erence between the squares of 8 and 9 is 17 = 8X2 + 1, and 23 X 2 + 1=47, which...
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A New System of Arithmetic, on an Improved Plan, Embracing the Rules of ...

Charles Guilford Burnham - 1857
...greatest square contained in 572 ; that is, it is the entire part of the root. This may be shown, thus : The difference between „ the squares of two consecutive numbers, is — equal to twice the less number, plus 1. The " difference between the squares of 8 and 9 is 17=8x2 + 1, and 23 x 2 + 1=47, which is...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1860 - 400 sider
...perfect square. But is the square of 12 the greatest perfect square contained in 168? That is, is 12 the entire part of the root? To prove this, we will...of two consecutive numbers, is equal to twice the lest number augmented by 1. Let a represent the less number, and a + 1, the greater. Then, (a + I)2...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1860 - 302 sider
...entire part of the root sought. For example, if it were required to extract the square root of 605, we should find 25 for the entire part of the root, and a remainder of 40, which shows that 605 is not a perfect square. But is the square of 25 the greatest perfect square contained in 665 ?...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1861 - 303 sider
...entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root,...the root? To prove this, we will first show that, thi difference between the squares of two consecutive numbers, it equal to twice the less number augmentel...
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