Decimal Approximation using Radical Expression

[Angela123]

Use [Delta]y=f'(x)[Delta]x to find a decimal approximation of the radical expression (730)^(1/6)

square root of 729=27

1/((1/6)x^(-5/6)) + 27 so I got 26.8611

I don't feel like I did this right.

 

[PAULK]

Use [Delta]y=f'(x)[Delta]x to find a decimal approximation of the radical expression (730)^(1/6)

square root of 729=27

1/((1/6)x^(-5/6)) + 27 so I got 26.8611

I don't feel like I did this right.

Neither do I. Start by using:

f(x) = x^(1/6)
x0 = 729 (yes, good idea)
dx = 1
Now

f(730) = f(729) + 1 * f'(729)

However, f(729) = 729^(1/6) = 3, not 27.
So look for an answer slightly bigger than 3.