Practical Lessons in Algebra, Elementary

Practical Lessons in Algebra, Elementary

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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. 1903 edition. Excerpt: ... + xy. 34. (1+x) 35. (1--x) 36. (x--2)'. 37. (x + 3)4. 38. (x-ryy. EVOLUTION. LESSON 83. The teacher will explain that finding a root is the converse of finding a power, and therefore that the root of a number may be found by reversing the operation of the preceding lesson. Examples: The square root of 25a;6y4=5a, 'V, because (5x3y2y=: 25. The cube root of--64x6i/3 =--kx?y. because (-4x'yf-Mafy..". Any root of a monomial may be found by taking the required root of the numerical coefficient, annexing the letters, giving each an exponent equal to its given exponent divided by the index of the root. Show that as even powers of both + and--. quantities are +, .. an even root may be either + or--, and that as all odd powers have the sign of the number raised, .'. all odd roots will have the sign of the given number. Show also that as no quantity raised to an even power can be--, .. there can be no even root of a--quantity. When such a root is indicated, it Ib called an imaginary quantity. Examples: The cube root of 8a;6=&c', of The fourth root of 1(te13= 2a. The fourth root of-16a;l2 is impossible. Show that the radical sign (4/) is used to indicate that the square root of the numbers over which it is placed is to be taken, as 4/g=3. To-indicate any other root a small figure is placed in the opening of the sign, as 27=3. t. Let the pupil solve the following examples if possible by inspection: Definitions. Evolution is the process of finding one of the equal factors of a number. The square root of a number is one of its two equal factors. The cube root of a number is one of its three equal factors. A radical quantity is one whose root is indicated, as 4/12. A rational quantity is an indicated root of a perfect power, as yl6, which=4. A surd...show more

Product details

  • Paperback | 26 pages
  • 189 x 246 x 1mm | 68g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236649680
  • 9781236649683