Use a linear approximation to estimate the number (8.07) ^2/3.

So let f (x) = x^ (2/3)

Then let f' (x) = 2/3 x^ (-1/3) = 2 / (3x^ (1/3))

When x = 8,

f (8) = 8^ (2/3) = 4

f' (8) = 2 / (3*8^ (1/3)) = 1/3

So near x = 8, the linear approximation is

f (x) ≈ f (8) + f' (8) (x - 8)

f (x) ≈ 4 + 1/3 (x - 8)

So the linear approximation for x = 8.03 is ...

f (8.03) ≈ 4 + 1/3 (8.03 - 8)

f (8.03) ≈ 4 + 1/3 (0.03)

f (8.03) ≈ 4.01

8.03^ (2/3) ≈ 4.01