 Hello friends, let's work out the following problem. It says using differentials find approximate value of the following up to three places of decimal. So let's now move on to the solution. And let us first define y as a function of x and here we define y as x to the power 1 by 4. And here we choose x in such a way so that we can easily find out its fourth root. And since we know 4 to the power 4 is 256. So we take it to be 256. And since we need to have x plus delta x as 255, we take delta x as minus 1. So x plus delta x is equal to 255. And we know that delta y is equal to f of x plus delta x minus fx. So this is x plus delta x to the power 1 by 4 minus x to the power 1 by 4. So we have delta y equal to 255 to the power 1 by 4 minus 256 to the power 1 by 4. So this implies 255 to the power 1 by 4 equal to delta y plus 256 to the power 1 by 4. Now 256 can be written as 4 to the power 4 and its power 1 by 4. So here 4 gets cancelled with 4 and we have delta y plus 4. Now we know that delta y is approximately equal to dy and delta y then given by dy by dx into delta x. Now y is x to the power 1 by 4. So dy by dx will be 1 by 4 into x to the power 1 by 4 minus 4. That is x to the power minus 3 by 4 into delta x. And delta x here is minus 1. So this is equal to 1 by 4 into x to the power 3 by 4 into minus 1. Let us now substitute the value of x here. So we have 1 by 4 into 256 to the power 3 by 4. So this is equal to minus 1 upon 4 into 256 can be written as 4 to the power 4 and its power 3 by 4. So this is equal to minus 1 by 4 into 4 to the power 3 and this is equal to minus 1 upon 256. Now 255 to the power 1 by 4 is equal to delta y plus 4. Now delta y is minus 1 upon 256 plus 4. This is equal to 1023 upon 256 and this is equal to 3.9961 approximately. So the value of approximate value of 255 to the power 1 by 4 is 3.9961. So this completes the question on this session. Bye for now. Take care and have a good day.