 Hello and welcome to the session. Let's work out the following problem. It says using the French use find the approximate value of the following up to three places of the SNL. And the here given number is 401 to the power 1 by 2. Let's now move on to the solution and let us define a function y in terms of x and here we define y equal to x to the power 1 by 2 and here we choose x in such a way so that we can easily find out its square root and that is also near to 401 so we choose x as 400 and since we need to have x plus delta x as 401 we choose delta x as 1 so x plus delta x is equal to 401. Now 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 2 minus x to the power 1 by 2 so this is equal to 401 to the power 1 by 2 minus 400 to the power 1 by 2 so this implies 401 to the power 1 by 2 equal to delta y plus 400 to the power 1 by 2 now 400 can be written as 20 to the power 2 and it's power 1 by 4. Now to get cancelled with 2 and we have delta y plus 20 now we know that delta y is approximately equal to dy and dy is equal to dy by dx into delta x so delta y is equal to dy by dx into delta x now y is x to the power 1 by 2 so dy by dx is equal to 1 by 2 into x to the power minus 1 by 2 into delta x which is 1 so this is equal to 1 by 2 into x to the power 1 by 2 into 1 let us now substitute the value of x here so this is 2 into 400 to the power 1 by 2 1 by 2 into 400 to the power 1 by 2 will be 20 as 400 can be written as 20 square 2 to gets cancelled and we have 20 so this is 1 by 40 so delta y is 1 by 40 now 401 to the power 1 by 2 is equal to delta y that is 1 by 40 plus 20 so this is equal to 801 by 40 and this is equal to 20.025 hence the approximate value of 401 to the power 1 by 2 is 20.025 so this completes the question and the session bye for now take care have a good day