Question

using approximation method approximate (255)^1/3

Answer 1

(255^1/3)=(6^3+39)^1/3=6(1+39/216)^1/3 =6(1+(1/3)*(39/216))=6(1+13/216)=6•36

Answer 2

Answer:

Step-by-step explanation:

del y= f(x+del x) - f(x)

here (255)^1/3=f(x+ del x)

dy/dx=del y/ del x

from above del y= dy/dx * del x

suppose you have  y=x^1/3

then dy/dx=1/3 x^-2/3

here x=216 because it is the nearest perfect cube

therefore= dy/dx=1/3(216)-2/3

dy/dx=1/3(1/216)^2/3)

dy/dx=1/3(1/36)=1/108

del y=dy/dx * del x

=1/108*(255-216)

=1/108*36

=0.36

therefore f(x+ del x)=255^1/3=0.36+6

=6.36