... 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 116av Bourdon (Louis Pierre Marie, M.) - 1838 - 355 siderUten tilgangsbegrensning - Om denne boken
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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 ?... | |
| 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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