New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges |
From inside the book
Results 1-5 of 35
Page vi
... RADICALS . Reduction 169 Addition 175 Subtraction . 176 Multiplication . 178 Division 180 Powers 181 Roots . 183 Rationalization 184 Imaginary Quantities . 188 Properties of Quadratic Surds 192 Radical Equations 196 QUADRATIC EQUATIONS ...
... RADICALS . Reduction 169 Addition 175 Subtraction . 176 Multiplication . 178 Division 180 Powers 181 Roots . 183 Rationalization 184 Imaginary Quantities . 188 Properties of Quadratic Surds 192 Radical Equations 196 QUADRATIC EQUATIONS ...
Page 12
... radical . Thus , 2 is the index of the square root , 3 of the cube root , and so on . over When the radical sign has no index written it , the index 2 is understood . Thus , a is the same as Va . A fractional exponent is also used to ...
... radical . Thus , 2 is the index of the square root , 3 of the cube root , and so on . over When the radical sign has no index written it , the index 2 is understood . Thus , a is the same as Va . A fractional exponent is also used to ...
Page 168
... RADICALS . 230. A RADICAL is a root of a quantity indicated ei- ther by a radical sign or by a fractional exponent ; as , √a , at , and 21+ a . When the root indicated can be exactly obtained , it is called a rational quantity , and ...
... RADICALS . 230. A RADICAL is a root of a quantity indicated ei- ther by a radical sign or by a fractional exponent ; as , √a , at , and 21+ a . When the root indicated can be exactly obtained , it is called a rational quantity , and ...
Page 169
... radical is denoted by the index of the radical sign , or by the denominator of the frac- tional exponent . Thus , √a , √y , ( abc ) , are radicals of the second degree ; ✓x2 , b3 , ( 2 u2x23y ) 3 , are radicals of the third degree ...
... radical is denoted by the index of the radical sign , or by the denominator of the frac- tional exponent . Thus , √a , √y , ( abc ) , are radicals of the second degree ; ✓x2 , b3 , ( 2 u2x23y ) 3 , are radicals of the third degree ...
Page 170
... radical sign into two factors , one of which , 27 a3 x " , is the greatest perfect cube contained in the radical quantity , and the other the surd 2 ax . But 27 a 3 ax ; consequently , by 3 = the general principle ( Art . 235 ) , the ...
... radical sign into two factors , one of which , 27 a3 x " , is the greatest perfect cube contained in the radical quantity , and the other the surd 2 ax . But 27 a 3 ax ; consequently , by 3 = the general principle ( Art . 235 ) , the ...
Contents
102 | |
106 | |
109 | |
119 | |
121 | |
126 | |
135 | |
141 | |
148 | |
155 | |
163 | |
169 | |
175 | |
181 | |
188 | |
196 | |
200 | |
206 | |
217 | |
280 | |
289 | |
296 | |
303 | |
311 | |
314 | |
321 | |
324 | |
327 | |
334 | |
340 | |
347 | |
358 | |
364 | |
372 | |
381 | |
388 | |
394 | |
Other editions - View all
Common terms and phrases
a²x² algebraic arithmetical progression binomial factors bushels cent Clearing of fractions coefficient common difference common logarithm Completing the square cube root decimal degree denominator denote Divide dividend equal equation Art EXAMPLES exponent expression Extracting the square Find the cube Find the square Find the sum find the values formula given equation Given x² greatest common divisor Greenleaf's imaginary inequality infinite series last term least common multiple logarithm loge miles Multiply negative nth root number of terms obtain OPERATION permutations polynomial positive problem proportion quadratic equation quan quotient radical sign ratio Reduce remainder required root Required the number required to find result rods second term simplest form solution square root Subtracting tity Transposing and uniting unknown quantity Whence whole number α₁
Popular passages
Page 41 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 61 - The LEAST COMMON MULTIPLE of two or more quantities is the least quantity that can be divided by each of them without a remainder.
Page 157 - Subtract the square of the root from the left period, and to the remainder bring down the next period for a dividend. 3d. Double the root already found, and place it on the left for a divisor. Find how many times the divisor is contained...
Page 79 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 141 - Hence, for raising a monomial to any power, we have the following RULE. Raise the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Page 82 - A Complex Fraction is one having a fraction in its numerator, or denominator, or both. It may be regarded as a case in division, since its numerator answers to the dividend, and its denominator to the divisor.
Page 275 - ... travel over, who gathers them up singly, returning with them one by one to the basket ? Ans.
Page 165 - Find the cube root of the first term, write it as the first term of the root, and subtract its cube from the given polynomial.
Page 255 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 316 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.