Using differentials, find the approximate value of each of the following up to 3 places of decimal.(iii) √0.6 (iv) ∛(0.009)
Using differentials, find the approximate value of each of the following up to 3 places of decimal.(iii) √0.6 (iv) ∛(0.009)

(iii) 

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 0.8 – 0.025 = 0.775.

(iv) 

Let  ……….(i)

   = 

     ……….(ii)

Now, from eq. (i), 

Here,  and ,

then 

 

Since,  and  is approximately equal to  and  respectively.

 From eq. (ii),  

 = 0.0083

Therefore, approximately value of  is 0.2 + 0.0083 = 0.2083.