 ... the 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, and a remainder of 40, which shows that 665 is not a perfect square. But is the square of 25...  Elements of Algebra - Page 114by Charles Davies - 1842 - 358 pagesFull view - About this book
 | Charles Davies - Algebra - 1835 - 378 pages
...665 is not a perfect square. But is the square of 25 the greatest perfect square contained in 665 1 that is, is 25 the entire part of the root ? To prove...the squares of two consecutive numbers, is equal to tvAce the less number augmented by unity. Let . . . a = the less number, and . . . o+l = the greater.... | |
 | Algebra - 1838 - 372 pages
...entire pun of liie root sought. For example, if it were required to extract the square root of 663. we should find 25 for the entire part of the root...numbers, is equal to twice the less number augmented by unify. Let . . . a = the less number, and . . . a + 1 = the greater. Then . . (a+l)3=a*+2a+l and .... | |
 | Charles Davies - Algebra - 1839 - 264 pages
...for a new divisor, and continue the operation, as before, until all the periods are brought down. 97. 1st REMARK. If, after all the periods are brought...equal to twice the less number augmented by unity. QUEST. — 96. Give the rule for extracting the square root of numbers. What is the first step ? What... | |
 | Algebra - 1839 - 368 pages
...of the greatest perfect square contained in the given number, or ike entire part of the root sougld. For example, if it were required to extract the square...augmented by unity. Let . . . a = the less number, and . . .o+1= the greater. Then . . (a+l)3=a3+2a+l and . . . (a)3=a3 Their difference is . = 2a+l as enunciated.... | |
 | Charles Davies - Algebra - 1839 - 272 pages
...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...equal to twice the less number augmented by unity. QUEST. — 96. Give the rule for extracting the square root of numbers. What is the first step ? What... | |
 | Charles Davies - Algebra - 1841 - 264 pages
...square of 25 the greatest perfect square contained in 665 ? that is, is 25 the entire part of the root 1 To prove this, we will first show that, the difference...augmented by unity. Let . . a= the less number, and . . a+ 1 = the greater. Then . (a+l)2 = a^+2a+l, and . . a2=a2. Their difference is = 2a+ 1 as enunciated.... | |
 | Charles Guilford Burnham - Arithmetic - 1841 - 324 pages
...that is, it is the 129 entire part of the root. This may be shown, thus : The difference be43 tween 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 23X2-}-1 =47, which is greater... | |
 | Charles Davies - Algebra - 1842 - 284 pages
...for a new divisor, and continue the operation as before, until all the periods are brought down. 97. 1st REMARK. If, after all the periods are brought...equal to twice the less number augmented by unity. QUEST. — 96. Give the rule for extracting the square root of numbers. What is the first step ? What... | |
 | Davis Wasgatt Clark - 1844 - 394 pages
...1 ; whence the square of a quantity greater by unity than a exceeds the square of a by 2o+ 1 ; or, the difference between the squares of two consecutive...equal to twice the less number augmented by unity. Hence the entire part of the root cannot be augmented unless the remainder exceed twice the root found... | |
 | William Scott - Algebra - 1844 - 568 pages
...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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