Using differentials, find the approximate value of each of the following up to 3 places of decimal. (ix) (82)^1/4 (x) (401)^1/2
Using differentials, find the approximate value of each of the following up to 3 places of decimal. (ix) (82)^1/4 (x) (401)^1/2

(ix) 

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  = 3.0092.

(x) 

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  = 20.025.