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# Use Newton's method to approximate the given number correct to eight decimal places.$\sqrt[8]{500}$

## $$\sqrt[8]{500} \approx 2.17455928$$

Derivatives

Differentiation

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the first thing we can do is take the derivative. Now we know that X one. We can estimate three approximately two point Duke's. It's close to two. However, it's greater than two in less than three, therefore exit to plugging in 2.2 Linus off of 2.2. Divide by a prime of 2.2 gives US 2.17 Ex of three gives US 2.17 except four gives US 2.17 and Exit five also gives us 2.17 We just at this point that we know our solution must be acts as 2.17 and then the correct number of decimal places it would be thus.