Question

find the cube root of (-4)
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Answer 1

Answer:

The nth root of N is a root of xn−N=0. The derivative of xn−N is nxn−1, so given an initial estimate, x, of the root, a closer estimate using Newton's method is

F(x)=x−xn−Nnxn−1=(n−1)x+Nxn−1n,

which is the average of x,x,…,x,n-1 of these and Nxn−1. This weighted average makes sense once you realize that both x and Nxn−1 are estimates of the nth root of N, that they are “off” in opposite directions, and that x is an n−1 times better estimate than Nxn−1.

Now, let’s apply the method…

Let N=4. Let x be your estimate of the cube root of 4. Start with a good guess, such as x=2. Then calculate

F(x)=2x+Nx23 to get a better estimate.

In this case,

F(2)=2×2+4223=53≈1.66666667…

Then, repeat using x=53

F(53)=2×53+4×32523=358225≈1.5911111...

This is approximation is good to about 3 significant digits, so let’s do it one more time,

F(358225)=2×358225+4×225235823=3433198121627675≈1.58740969614163...

Explanation:

Hope it will help you!!! Kindly mark my Answer as Brainliest......

Answer 2

Answer:

-64

Step-by-step explanation:

(-4)^3

= -64

I hope it is right