Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xi) (0.0037)^1/2 (xii) (26.57)^1/3
Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xi) (0.0037)^1/2 (xii) (26.57)^1/3

(xi) 

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 0.06 +  = 0.060833.

(xi) 

Let  ……….(i)

   = 

     ……….(ii)

Now, from eq. (i), 

Here,  and ,

then 

 

Since,  and  is approximately equal to  and  respectively.

 From eq. (ii),  

 = 0.0159

Therefore, approximately value of  is 3 – 0.0159 = 2.9841.