An Elementary Algegra

An Elementary Algegra

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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. 1873 edition. Excerpt: ...root of the coefficient of the given quantity, and divide the exponents of its letters by 2. The square root thus found, which may be either positive or negative (Art. 244, 2), is 6ab 3. Find the fourth root of 81a;y. Ans. 3x2y. 216. Rule for Evolution of Monomials.--Extract the required root of the numerical coefficient, divide the exponent of each letter by the number denoting the index of the required root, and give the proper sign to the result. The root of a fraction is found by taking the root of the numerator and of the denominator. PROBLEMS. 1. What is the cube root of-8x"y6? Ans.-2xy2. 2. What is the fourth root of 625ay? 3. What is the cube root of-2Wc12? Ans.-2a2V. 4. Find the cube root of-64a6yi. Ans.--4a2y. 5. Find the rath root of 7"aV. 6. Find the fifth root of aV. Ans. Jx 7. What is the value of 1y625yz12? CASK II. Square Root of Polynomials. 217.--Ex. 1. Find the square root of a? + 2ab + b Solution. From the nature of the a?+2ab + ba + b square of a polynomial (Art. 239, Prin. 2), a' the first term of the given square will be 2a ) 2ab + b2 the square of the first term of the required (2a + 6)6 = 2ab + 62 root. The first term of the square is a," and its square root is a, which we write as the first term of the root. Subtracting a2 from the whole expression, we have left 2a6 + 62, which must be two times the product of the two terms of the root plus the square of the last term of the root (Art. 239, Prin. 2). Dividing 2a6, the first term of the dividend, by 2a, which is double the first term of the root, we obtain 6, the other, or second, term of the root. Adding the 6 to the trial divisor 2a, we obtain the complete divisor 2a + 6. Multiplying this by 6, the second term, and subtracting, we have more

Product details

  • Paperback | 46 pages
  • 189 x 246 x 3mm | 100g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236610024
  • 9781236610027