Elements of Algebra: Including Sturms' Theorem |
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Page 8
... Cube Roots of Numbers .. 209-213 To Extract the nth Root of a Whole Number . 213-215 Extraction of Roots by Approximation .. 215-218 Cube Root of Decimal Fractions . 218 Any Root of a Decimal Fraction . 219 Formation of Powers and ...
... Cube Roots of Numbers .. 209-213 To Extract the nth Root of a Whole Number . 213-215 Extraction of Roots by Approximation .. 215-218 Cube Root of Decimal Fractions . 218 Any Root of a Decimal Fraction . 219 Formation of Powers and ...
Page 14
... root is to be extracted . Thus , 2 Va or simply a denotes the square root of a . 3 Va denotes the cube root of a . Va denotes the fourth root of a . The number placed over the radical sign is called the index of the root . Thus , 2 ...
... root is to be extracted . Thus , 2 Va or simply a denotes the square root of a . 3 Va denotes the cube root of a . Va denotes the fourth root of a . The number placed over the radical sign is called the index of the root . Thus , 2 ...
Page 207
... Cube Root of Numbers . 209. The cube or third power of a number , is the product which arises from multiplying the number twice by itself . The cube root , or third root of a number is either of three equal factors into which it may be ...
... Cube Root of Numbers . 209. The cube or third power of a number , is the product which arises from multiplying the number twice by itself . The cube root , or third root of a number is either of three equal factors into which it may be ...
Page 208
... cube root will be expressed by a whole number , plus an irrational number , as may be shown by a course of rea ... cube of 90 and the cube of 89 , is equal to 3 ( 89 ) 2 + 3 x 89 + 1 = 24031 . 211. In order to extract the cube root ...
... cube root will be expressed by a whole number , plus an irrational number , as may be shown by a course of rea ... cube of 90 and the cube of 89 , is equal to 3 ( 89 ) 2 + 3 x 89 + 1 = 24031 . 211. In order to extract the cube root ...
Page 209
... cube of 100 , its root will be expressed by two figures , or by tens and units . Denoting the tens by a , and the units by b , we have ( Art . 198 ) , ( a + b ) 3 = a3 + 3a2b + 3ab2 +63 . Whence it follows , that the cube of a number ...
... cube of 100 , its root will be expressed by two figures , or by tens and units . Denoting the tens by a , and the units by b , we have ( Art . 198 ) , ( a + b ) 3 = a3 + 3a2b + 3ab2 +63 . Whence it follows , that the cube of a number ...
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affected algebraic quantities arithmetical means arithmetical progression binomial called co-efficient common difference consequently contain contrary signs cube root Cx² decimal deduced denominator denote divide dividend division entire number enunciation equa equal equation involving example exponent expression extract the square factors figure find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square permutations problem proportion proposed equation quan quotient radical sign Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose supposition take the equation third tion tities total number transposing unity unknown quantity whence whole number ах
Popular passages
Page 30 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 275 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 27 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 179 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 180 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 90 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 346 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 202 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.