Using differentials, find the approximate value of each of the following up to 3 places of decimal. (i)√ 25.3 (ii) √49.5
Using differentials, find the approximate value of each of the following up to 3 places of decimal. (i)√ 25.3 (ii) √49.5

Assume  ……….(i)

   = 

   ……….(ii)

Now, from eq. (i), 

Here,  and , then 

 

Since,  and  is approximately equal to  and  respectively.

 From eq. (ii),

 = 0.03

Therefore, approximately value of  is 5 + 0.03 = 5.03.

(ii) 

Let  ……….(i)

   = 

   ……….(ii)

Now, from eq. (i), 

Here,  and , then

 

Since,  and  is approximately equal to  and  respectively.

 From eq. (ii),  

= 0.0357

Therefore, approximately value of  is 7 + 0.0357 = 7.0357.