A Short Course in Higher Algebra: For Academies, High Schools, and CollegesLeach, Shewell, and Sanborn, 1889 - 426 σελίδες |
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Σελίδα vii
... Square Root of Polynomials Square Root of Numbers Cube Root of Polynomials Cube Root of Numbers • XIX . THE THEORY OF EXPONENTS XX . RADICALS PAGE 158 158 159 · 161 162 . 165 165 167 170 . 173 176 • 180 190 • · • 190 • 193 · · 195 196 ...
... Square Root of Polynomials Square Root of Numbers Cube Root of Polynomials Cube Root of Numbers • XIX . THE THEORY OF EXPONENTS XX . RADICALS PAGE 158 158 159 · 161 162 . 165 165 167 170 . 173 176 • 180 190 • · • 190 • 193 · · 195 196 ...
Σελίδα 53
... square root . Thus , since 9 a + b2 equals 3 a2b × 3 a2b , it is a perfect square , and 3 a2b is its square root . Note . 9a4b2 also equals -3a2b3a2b , so that its square root is either 3 a2b or -3a2b . In the examples in this chapter ...
... square root . Thus , since 9 a + b2 equals 3 a2b × 3 a2b , it is a perfect square , and 3 a2b is its square root . Note . 9a4b2 also equals -3a2b3a2b , so that its square root is either 3 a2b or -3a2b . In the examples in this chapter ...
Σελίδα 54
... square ( Art . 108 ) . 1. Factor a2 + 2 ab2 + b1 . By Art . 109 , the square root of the expression is a + b2 . Hence , a2 + 2 ab2 + b1 = ( a + b2 ) ( a + b2 ) , or ( a + b2 ) 2 , Ans . 2. Factor 422-12xy +9 y2 . 4x2 - 12xy + 9y = ( 2x ...
... square ( Art . 108 ) . 1. Factor a2 + 2 ab2 + b1 . By Art . 109 , the square root of the expression is a + b2 . Hence , a2 + 2 ab2 + b1 = ( a + b2 ) ( a + b2 ) , or ( a + b2 ) 2 , Ans . 2. Factor 422-12xy +9 y2 . 4x2 - 12xy + 9y = ( 2x ...
Σελίδα 55
... square root of the first term and of the last term ; add the results for one factor , and subtract the second result from the first for the other . 1. Factor 3622 — 49 y2 . The square root of the first term is 6x , and of the last term ...
... square root of the first term and of the last term ; add the results for one factor , and subtract the second result from the first for the other . 1. Factor 3622 — 49 y2 . The square root of the first term is 6x , and of the last term ...
Σελίδα 165
... root of the quantity is to be found . Thus , va indicates the second or square root of ɑ ; Va indicates the third or cube root of a ; Va indicates the fourth root of a ; and so on . The index of the root is the figure written over the ...
... root of the quantity is to be found . Thus , va indicates the second or square root of ɑ ; Va indicates the third or cube root of a ; Va indicates the fourth root of a ; and so on . The index of the root is the figure written over the ...
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Άλλες εκδόσεις - Προβολή όλων
A Short Course in Higher Algebra: For Academies, High Schools, and Colleges Webster Wells Προβολή αποσπασμάτων - 1889 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ab² annuity arithmetical means arithmetical progression Binomial Theorem cent compound interest Clearing of fractions coefficient cologarithms common logarithm continued fraction convergent cube root decimal point denominator denote derive the formula digits divided divisor eighth term equal EXAMPLES Expand exponent expression Extracting the square find the logarithm find the number Find the value following equations following rule geometrical means geometrical progression given equation Given log harmonical means Hence increased integral interest being compounded last term mantissa Multiplying Note number corresponding number of combinations number of permutations number of terms obtain partial fractions present value quadratic quadratic equation quantities taken quotient radical sign remainder Required the number result second member second term Solve the equation Solve the following square root Subtracting unknown quantity Whence
Δημοφιλή αποσπάσματα
Σελίδα 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Σελίδα 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Σελίδα 269 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 129 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.
Σελίδα 267 - 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.
Σελίδα 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Σελίδα 227 - A courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.
Σελίδα 44 - 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.
Σελίδα 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.
Σελίδα 136 - Find the value of one of the unknown quantities, in terms of the other and known quantities...