Math Help - Use differentials to estimate the value of 30^(1/5)

1. Use differentials to estimate the value of 30^(1/5)

i know you need to find a nice number that would solve out but the only one i could find was 5 so 5^1/5 = 1. but when i try to put that value into the derivative (1/5)(5^-4/5) i get some random number so i must be doing something wrong! help??

2. Originally Posted by yess
i know you need to find a nice number that would solve out but the only one i could find was 5 so 5^1/5 = 1. but when i try to put that value into the derivative (1/5)(5^-4/5) i get some random number so i must be doing something wrong! help??
$f(x + h) \approx f(x) + h f'(x)$.

Take $f(x) = x^{1/5}$, x = 32, h = -2.

3. Or, you could just use the Binomial expansion.

$30^{1/5}=(32-2)^{1/5}=32^{1/5}(1-2/32)^{1/5}=2(1-1/16)^{1/5}$ and so on.