University Algebra; Embracing a Logical Development of the Science, with Numerous Graded Examples
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University Algebra; Embracing a Logical Development of the Science, with Numerous Graded Examples

University Algebra; Embracing a Logical Development of the Science, with Numerous Graded Examples


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1859 Excerpt: ...m/5 _ a" lb Whence, the RULE. Reduce the radicals to a common index; then divide the coefficient of the dividend by that of the divisor for a new coefficient, and the quantity under the radical sign in the dividend by that in the divisor for a new quantity under the radical sign, leaving the index unchanged. EXAMPLES. Perform the following indicated divisions: _ I3 /2. 133 ft 2g3 /Jo 1. a/ --TV j" Arts. 3 V 3 4 V 5 39V 3 2-7/e + H/7.' Ans.----=--. 4 V 5 7 V 2 12 V 25 30 The two results are identical; but the second one has Deen obtained by following the ordinary rule for exponents. Hence, we conclude that the operation for division is the same whether the exponents are entire or fractional. Ans. 8xT + 2x2y + xy2 + y3. KEDUCTIOT OF EADICALS. 135. It is often useful to transform radical expressions of the form 7= 1=, and 1= 7=-, into yb + yc yb--yc equivalent expressions, in which the denominator is rational, that is, when it contains no radical expressions. The first form may be thus transformed, by multiplying both terms by y%--/c; and the second, by multiplying both terms by y%+ i/c, giving ayT)--a-y/c, ay% + ay/c j, ana j b--c b--e If only one term of the denominator is affected by a radical, the same rule will hold good. EXAMPLES. Render the denominators of the following fractions rational: 2. 2V3-2Vr4 TfTTT Ans-3-4 2. -_. Ans.!4 V?. Ans.-+ /r--1. x V x2 136. In the solution of certain equations, it oftentimes becomes necessary to extract the square root of expressions of the form, a + /b, and a--./b. In some cases, this operation may be performed, in other cases it cannot be performed. To investigate a rule for determining when the operation can be performed, and the manner of performing it, assume J a + Jb--x + y (1.) y/a-fb =...


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Product Details
  • ISBN-13: 9781231111055
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 48
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1231111054
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 104 gr


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University Algebra; Embracing a Logical Development of the Science, with Numerous Graded Examples
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