The value of `(127)^(1//3)` to four decimal places, is

Options

A. `5.0267`
B. `5.4267`
C. `5.5267`
D. `5.001`

Answer

A

Explanation

Let `y=x^(1//3), x=125 and x+ Delta x =127`. Then,
`dy/dx=1/(3x^(2//3)) Delta x = 2`
When, x =125, we have
`y=5 and dy/dx=1/75`
`:." "Deltay=dy/dx Deltax rArr Deltay= 1/75 xx2=2/75`
`:." "(127)^(1//3) = y+ Deltay=5+2/75=5+8/3 xx1/100`
`rArr" "(127)^(1//3) = 5+(2.6667)/100=5.02667 cong 5.0267`