Higher AlgebraFisher and Schwatt, 1901 - 615 páginas |
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Página xii
... Square Roots of Simple Binomial Surds 290 Approximate Values of Surd Numbers . 291 CHAPTER XX . IMAGINARY AND COMPLEX NUMBERS . Imaginary Numbers Complex Numbers Complex Factors Square Root of a Complex Number 294 298 301 301 CHAPTER ...
... Square Roots of Simple Binomial Surds 290 Approximate Values of Surd Numbers . 291 CHAPTER XX . IMAGINARY AND COMPLEX NUMBERS . Imaginary Numbers Complex Numbers Complex Factors Square Root of a Complex Number 294 298 301 301 CHAPTER ...
Página 239
... root of a3 +3 a2b + 3 ab2 + b3 . A second root of a number is usually called a square root ; and a third root a cube root . 2. It follows from the definition of a root that a qth root of a number is one of q equal factors of the number ...
... root of a3 +3 a2b + 3 ab2 + b3 . A second root of a number is usually called a square root ; and a third root a cube root . 2. It follows from the definition of a root that a qth root of a number is one of q equal factors of the number ...
Página 241
... root of the positive number which has the same absolute value , and prefix ... square is - 16 . Consequently -16 cannot be expressed in terms of the ... root , and when q is even at least two ; also that any negative number , which is an ...
... root of the positive number which has the same absolute value , and prefix ... square is - 16 . Consequently -16 cannot be expressed in terms of the ... root , and when q is even at least two ; also that any negative number , which is an ...
Página 242
George Egbert Fisher, Isaac Joachim Schwatt. Write 1. Two square roots of 49 . EXERCISES I. 3. Two sixth roots of 64 . Write one cube root of 5. 64 . 6. - 125 . 2. Two fourth roots of 81 . 4. Two square roots of 5o . 7. 1000 . 8. - am ...
George Egbert Fisher, Isaac Joachim Schwatt. Write 1. Two square roots of 49 . EXERCISES I. 3. Two sixth roots of 64 . Write one cube root of 5. 64 . 6. - 125 . 2. Two fourth roots of 81 . 4. Two square roots of 5o . 7. 1000 . 8. - am ...
Página 245
... root of the radicand taken positively . Ex . 1 . Therefore √ ( 16 a2b1 ) = √16 × √a2 × √b1 = 4ab2 , the principal square root . ± √ ( 16a2b1 ) = ± 4 ab2 . In the following examples we shall give only the positive even roots . Ex ...
... root of the radicand taken positively . Ex . 1 . Therefore √ ( 16 a2b1 ) = √16 × √a2 × √b1 = 4ab2 , the principal square root . ± √ ( 16a2b1 ) = ± 4 ab2 . In the following examples we shall give only the positive even roots . Ex ...
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Higher Algebra George Egbert Fisher,Isaac J. 1867- jt. auth Schwatt Sin vista previa disponible - 2015 |
Términos y frases comunes
a₁ a²b a²x a²x² ab² algebraic arithmetical means arithmetical progression assigned number ax² b₁ binomial coefficient Commutative Law complex number continued fraction convergent corresponding cube root definition denominator determinant difference digits divided divisor equal equivalent EXERCISES exponent Find the values finite following expressions following principle geometrical progression given equation given expression given number given series given system greater harmonical means inequality integer irrational number less logarithm mantissa method miles multinomial multiplied negative number obtained parentheses positive integer positive number powers preceding article principal root quadratic equation quotient r₁ radicand rational number remainder required numbers result S₁ second member second term Simplify solution Solve the equation square root Substituting subtracted surds unknown number whence wherein x²y yards
Pasajes populares
Página 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Página 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 64 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Página 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.
Página 456 - ж2), etc-, are functions of x ; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 364 - The volume of a gas varies inversely as the pressure when the temperature is constant. When the pressure is 15, the volume is 20; what is the volume when the pressure is 20 ? Let v stand for the volume and p for the pressure. Then from pv = k we obtain k = 300. Therefore pv = 300. Consequently, when p = 20, 20 v = 300 ; whence v = 15. EXERCISES III. If zee y, what is the expression for x in terms of y, 1.
Página 379 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
Página 204 - A system of linear equations has a definite number of solutions. (i.) When the number of equations is the same as the number of unknown numbers. (ii.) When the equations are independent and consistent.
Página 100 - The square of the sum of two numbers is equal to the square \ (¿ of the first, plus twice the product of the first and second, plus the J square of the second.