2006-09-06 23:26:15 · 11 answers · asked by CHINMAY A 1 in Science & Mathematics ➔ Mathematics
5.9597345173478
5.9597345173478 * 5.9597345173478 *5.9597345173478 = 211.68
2006-09-06 23:35:05 · answer #1 · answered by Anonymous · 0⤊ 0⤋
To solve it without a scientific calculator and log tables, identify the cube closest to 211.68. this is 216= 6x6x6
write c. rt. 211.68 as c. rt. 216-4.32 or
6x c.rt. (1-4.32/216), i.e. 6 x c.rt. (1-0.02). Now use binomial theorem for powers other than natural numbers to expand this as
6 [1+1/3 x (-.02)+ 1/3 x (1/3 - 1) (-.02)^2 + 1/3 (1/3 - 1) (1/3 - 2) (-.02)^3+ 1/3 (1/3 - 1)(1/3 - 2)(1/3 - 3) (-.02)^4........]
=6 [1-.00667- .00009......] = 6 [1-0.00676]
=6-0.04056
=5.95944 (apprx.)
2006-09-07 00:13:11 · answer #2 · answered by Amit K 2 · 0⤊ 0⤋
5.59598 is the cube root of 211.687423755192 that's the close you can get
2006-09-06 23:39:53 · answer #3 · answered by Julio G 1 · 0⤊ 0⤋
There is Binomial theorem as well, see below:
(211.68)^1/3 = (216-4.32)^1/3 = 216^1/3 x(1-4.32/216)^1/3
=6x (1-0.02)^1/3 = 6x (1-1/3x0.02) = 6x (1-0.666667) = 6x 0.993333 = 5.96.
Please note no complex calculation or formula is involved, just multiplication, division and subtraction has been used.
2006-09-08 04:27:05 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Let's say, x^3 = 211.68
So, 3log(x) = log(211.68)
From Scientific calculator,
log(211.68) = 2.326
So, log(x) = 0.775
So, x = cube root of(211.68) = Inv log(0.775) = 5.9597
2006-09-06 23:37:54 · answer #5 · answered by M1976 2 · 0⤊ 0⤋
I assume u have a Scientific calculator...
unless u want me to find it for u in terms of rational numbers...;)
2006-09-06 23:31:49 · answer #6 · answered by â? MÎ?Я©ỮÅ?Â¥ â?¢ â? 3 · 0⤊ 0⤋
5.9597345173478
2006-09-08 17:42:55 · answer #7 · answered by Anonymous · 0⤊ 0⤋
5.95973033
2006-09-06 23:37:16 · answer #8 · answered by Anonymous · 1⤊ 0⤋
5.9597
2006-09-09 20:21:01 · answer #9 · answered by Anonymous · 0⤊ 0⤋
5.95973
2006-09-06 23:52:55 · answer #10 · answered by KC 1 · 0⤊ 0⤋