Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and CollegesWinthrop B. Smith & Company, 1852 - 396 σελίδες |
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Σελίδα vii
... ROOTS- RADICALS - INEQUALITIES . Involution or Formation of Powers ..... SQUARE ROOT of Numbers - Of Fractions 172 .173-177 Perfect and Imperfect Squares - Theorem ..178-179 Approximate Square Roots ...... 180 Square Root of Monomials ...
... ROOTS- RADICALS - INEQUALITIES . Involution or Formation of Powers ..... SQUARE ROOT of Numbers - Of Fractions 172 .173-177 Perfect and Imperfect Squares - Theorem ..178-179 Approximate Square Roots ...... 180 Square Root of Monomials ...
Σελίδα 14
... root is called the square or second root , the cube or third root , the fourth root , & c . , according to the number of times it must be taken as a factor to produce the given quantity . Thus , 2 is the second or square root of 4 ...
... root is called the square or second root , the cube or third root , the fourth root , & c . , according to the number of times it must be taken as a factor to produce the given quantity . Thus , 2 is the second or square root of 4 ...
Σελίδα 18
... square root of m minus the square root of n . 10. The square root of m minus n . 11. The square root of m , minus n . 12. The square root of b squared , minus m plus n into c . 1. 5a + b2 . y 2. x + 3x 3 . 3z xty . 3x - ny 4 . m - n ...
... square root of m minus the square root of n . 10. The square root of m minus n . 11. The square root of m , minus n . 12. The square root of b squared , minus m plus n into c . 1. 5a + b2 . y 2. x + 3x 3 . 3z xty . 3x - ny 4 . m - n ...
Σελίδα 125
... square of a - b . 23. Find the cube of a - 3b . m3 - 3m2n + 3mn2 — n3 m3 - 6m2n + 12mn2 - 8n3 ° Ans . a2ab + 1b2 . Ans . { a3 — ‚ § ; b3 — 1a2b + 3ab2 . 1 24. Find the square of x- -1 . 25. Find the cube of x- 1 XC х 26 ... SQUARE ROOT . 125.
... square of a - b . 23. Find the cube of a - 3b . m3 - 3m2n + 3mn2 — n3 m3 - 6m2n + 12mn2 - 8n3 ° Ans . a2ab + 1b2 . Ans . { a3 — ‚ § ; b3 — 1a2b + 3ab2 . 1 24. Find the square of x- -1 . 25. Find the cube of x- 1 XC х 26 ... SQUARE ROOT . 125.
Σελίδα 126
... square root will be ONE . Again , take the numbers 10 , 20 , 30 , 40 , their squares are 80 , 90 , 100 ; 70 , 60 , 50 , 100 , 400 , 900 , 1600 , 2500 , 3600 , 4900 , 6400 , 8100 , 10000 . From this we see , that the square root of 100 ...
... square root will be ONE . Again , take the numbers 10 , 20 , 30 , 40 , their squares are 80 , 90 , 100 ; 70 , 60 , 50 , 100 , 400 , 900 , 1600 , 2500 , 3600 , 4900 , 6400 , 8100 , 10000 . From this we see , that the square root of 100 ...
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Άλλες εκδόσεις - Προβολή όλων
Ray's Algebra, Part Second: An Analytical Treatise, Designed for High ... Joseph Ray Πλήρης προβολή - 1857 |
Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic algebraic quantity arithmetical progression Binomial Theorem coëfficient continued fraction converging fraction cube root denominator denotes dividend divisible equa equal equation whose roots evident exactly divide EXAMPLES FOR PRACTICE exponent expressed extract the square Find the cube Find the greatest Find the number Find the square Find the sum find the value geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root nth term number of balls number of permutations number of terms operation perfect square polynomial positive root preceding proportion proposed equation quotient ratio real roots reduced remainder Required the numbers required to find result second degree second term square root Sturm's theorem substitute subtracted taken theorem third tion transformed transposing unknown quantity whence whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 42 - 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.
Σελίδα 39 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 128 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 43 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Σελίδα 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Σελίδα 140 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Σελίδα 220 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Σελίδα 183 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Σελίδα 28 - Multiply the coefficients of the two terms together, and to their product annex all the letters in both quantities, giving to each letter an exponent equal to the sum of its exponents in the two factors.