Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xiii) (81.5)^1/4 (xiv) (3.968)^3/2
Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xiii) (81.5)^1/4 (xiv) (3.968)^3/2

(xii) 

Let  ……….(i)

   = 

   ……….(ii)

Now, from eq. (i), 

  ……….(iii)

Here  and 

Then 

  = 

Since,  and  is approximately equal to  and  respectively.

 From eq. (ii),  

= 0.00462

Therefore, approximate value of  is 3 + 0.00462= 3.00462.

(xiv) 

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 8 – 0.096 = 7.904.