estimation of cube roots of 255 and correct to one decimal place?

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First establish the nearest integer cubes. In this case

6³ = 216
7³ = 343

216 < 255 < 343. So you know you will have an answer that is 6.x

To approximate what the tenth will be, simply take the difference of 6³ and 7³ =
343 - 216 = 127.
Now divide the difference between 255 into this.

255 - 216 = 39
39/127 = .307

This will round to .3, and you have your x. The answer then is 6.3 which you can confirm by taking 6.3³ = 250.04 and compare it to
6.4³ = 262.1.

Clearly 255 is closer to 250.04...Show more

Estimating Cube Roots...Show more

Remember this method - easy exam Q.

Nearest cube is 6^3 = 216
255 = 6^3 *(255/216) ~ 6^3 * 1.18
255^(1/3) = 6[(1 + .18)^(1/3)]
Now look at that. Last bit div by 3.
Teach' is trying to be helpful.
You get the marks for remembering
(1 + x)^(1/3) ~ 1 + x/3
255^(1/3) ~ 6(1 + .06)
255^(1/3) ~ 6.3(6) to one decimal place

Calculator says 255^(1/3) ~ 6.341

Regards - Ian...Show more

let f(x) = x^1/3

f'(x) = 1/3 x^(-2/3)

use the following approximation
{f(a + delta x) - f(a)} / delta x = f'(a)

let a = 250.047 so delta x = 4.953


as cube root of 250.047 is 6.3 u can use this somewhat accurately

and now u would ask how to think about this just find the cube of 1,2,3,4,5,6,7 u would probably remember them as u are giving NTSE

u would feel that cube root of 255 lies between 6 and 7 and that too nearer to 6 so just take about 6.1 , 6.2 , 6.3 , 6.4 u will definitely get this...Show more

I take it algebra, which you would be able to no longer understand calculus.. nather do I.. so for you to use the quadratic formula... opposite of b (sq. root) of b squared - 4ac divided by 2a minus 3x squared from the two aspects and make each little thing the alternative (it quite is much less confusing that way) and you come back up with 3x squared + - 2x + -2 = 0 3 = a, 2 = b and c. so.......... -2 |2 squared - 4(3)(2) / 2(3) the equation supply you 2 solutions. 2 squared is 4 minus -24 (upload 24.) that's 28. -2 |28 / 2(3) (that's six.) 28/6 is 4.sixty seven rounded to the 10th OR 4 2/3. sqaure root of four 2/3 is two.sixteen 02468 cases that by -2 and you come back up with your answer.. -4.324936.. when you consider which you around to the closest hundreth.. it may be -4.32...Show more