 It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether...  Algebra for Colleges and Schools - Page 161by Henry Sinclair Hall, Samuel Ratcliffe Knight - 1897 - 516 pagesFull view - About this book
 | John Bonnycastle - Algebra - 1813 - 456 pages
...Thus, л/а* = + a or — a, and Vi1 = + b or — ¿, &c. But the cube root, or any other odd root, of a quantity, will have the same sign as the quantity itself. Thus, V«3 = a; •l/ — a>= —a; and V — «5= —a, &c.(v) It may here, also, be farther remarked,... | |
 | John Bonnycastle - Algebra - 1818 - 284 pages
.... Thus, i/aa = + a or— a, and ^/64 = + b or — 6, &c. But the cube root, or any other odd root, of a quantity, will have the same sign as the quantity itself. Thus, a ; 3/_a3 = —a; and ^/— as = — a, &c.(o) (o) The reason why + a and — a are each the... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...necessarily positive. In fact, 2m being the formula of even numbers, we have ( ±a)Sm=[(i±-o)a] 281. Any odd power of a quantity will have the same sign as the quantity itself. For, the general formula of odd numbers, (Art. Ill), being 2m+l, we have 2mX ±a) =a2'"X 3=a=The involution... | |
 | James Ryan - Algebra - 1824 - 550 pages
...root ot «2m is equal to +a or or —a ; for (=i=«)2m==(=t«)3 X am=o?ra(Art. 280). 296. Any odd root of a quantity, will have the same sign as the quantity itself. Thus the (2m + l)th root root ofrta2™-!-1 is equal to=fca ; for (=i=a)*m+l is equal to ztn2""*-'... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...+ or — . Thus, \/a3=+a or —a, and y64=+6 or —6, &c. But the cube root, or any other odd root, of a quantity, will have the same sign as the quantity itself. Thus, 3/o3=a; 3/-a3 = — a; and y— a«=— a, &c.* It may here, also, be farther remarked, that... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 pages
...fourth root, or any other even root of an affirmative quantity, may be either + or — .(a) Any odd root of a quantity will have the same sign as the quantity itself. EXAMPLES. 1. Required \he square root of 16.r2.. Here, v/16=4, and v/a:* = *!=.r; . • . 4r is the... | |
 | James Ryan, Robert Adrain - Algebra - 1835 - 388 pages
...fact, 2m being the formula of even numbers, we have (±a)2m=[(±o)2]"'=(+a2)'"=+a-'n . . . (4). 220. Any odd power of a quantity will have the same sign as the quantity itself . For, the general formula of odd numbers, (Art. I11), being 2ra+1, we have (±o)2m+' = (±o)2"'X(±a)... | |
 | John Bonnycastle - 1848 - 334 pages
...Thus, \/aa = + a or — a, and ty b* = + 62 or — 62, &c. But the cube root, or any other odd root, of a quantity, will have the same sign as the quantity itself. Thus, It may here, also, be further remarked, that any even root of a negative quantity is unassignable.... | |
 | John Bonnycastle - Algebra - 1851 - 288 pages
...Thus ^/ a 2 == + a or — #, and \/ b* = -f b or — b, &c. But the cube root, or any other odd root, of a quantity, will have the same sign as the quantity itself. Thus, ya 3 = a ; V — fl3 = — a J an( * V — ^ = — °", & c -* It may here, also, be farther... | |
 | Benjamin Greenleaf - Algebra - 1852 - 348 pages
...minus. Thus, */a*=-\-a or —a ; and 4 */b 4 =-\-b or —b. But the cube root, or any other odd root of a quantity, will have the same sign as the quantity itself. Thus 3 \/a 3 =a ; 3 /\/—a 3 = —a, and 5 */—a 5 =—a. The reason why -\-a and —a are rach the... | |
| |
