Approximate Value - Cube Root

Category: Differential Calculus, Arithmetic

"Published in Newark, California, USA"

Find the approximate value of ∛200 without using a calculator.

Solution:

Well, we know that

             1³ = 1

             2³ = 8

             3³ = 27

             4³ = 64

             5³ = 125

             6³ = 216       and so on.

Since 200 is between 125 and 216, the ∛200  is between 5 and 6. We can get the approximate value of ∛200  without using a calculator as follows

Let

then

If   x = 216 (please choose this number because it is close to 200)
   dx = 200 - 216 = -16

then dy will be

Therefore

using a calculator

and using a scientific calculator

which is close to the final answer.