Using differentials, find the approximate value of each of the following up to 3 places of decimal. (vii) (26)^1/3 (viii) (255)^1/4

(vii) 

Let  ……….(i)

   = 

    ……….(ii)

Now, from eq. (i), 

= 

Here,  and ,

then  = 

 

Since,  and  is approximately equal to  and  respectively.

 From eq. (ii),   = 

Therefore, approximately value of  is  = 2.9629.

(viii) 

Let  ……….(i)

   = 

   ……….(ii)

Now, from eq. (i), 

= =  ……….(iii)

Here  and 

Then 

= 

 = 

Since,  and  is approximately equal to  and  respectively.

 From eq. (ii),  

Therefore, approximate value of  is  = 3.9961.