 Hello and welcome to the session. In this session we will discuss a question which says that using binomial theorem evaluate 1 over root 0.7 to 3 places of decimals. Now before starting the solution of this question we should know some results. If we have to find the LF root of any number capital N then this can be written as a raised to power n plus b whole raised to power 1 by n. Where a n is nearest to n and b which is either positive or negative is very small in comparison to a raised to power n. Now for expanding this we have to make the first term equal to unity. So this can be written as a raised to power n whole raised to power 1 by n within brackets 1 plus b over a raised to power n whole raised to power 1 by n. Now on expanding this an approximate value of the root can be obtained. Secondly we should know the expansion of a binomial expression and that is 1 plus x raised to power n is equal to 1 plus nx plus n into n minus 1 over 1 into 2 into x square plus n into n minus 1 into n minus 2 over 1 into 2 into 3 into x cube plus so on up to infinity. Where absolute value of x is less than 1 and n be any fraction. Now these results will work out as a key idea for solving out this question. And now this will start with the solution. Here we have to evaluate 1 over root 0.7. Now 1 over root 0.7 can also be written as 1 over 0.7 raised to power 1 by 2 which can further be written as 0.7 raised to the power minus 1 by 2. Now 0.7 raised to power minus 1 by 2 can be written as 0.7 here can be written as 1 minus 0.3 over raised to power minus 1 by 2. Now we have written it in this form. Where capital N is 0.7, a raised to power n is 1 and b is minus 0.3. Now we have to expand 1 minus 0.3 over raised to power minus 1 by 2 and for this we will be using the expansion which is given in the key idea. Now comparing here x is minus 0.3 and n is minus 1 by 2. So all extending 1 minus 0.3 over raised to power minus 1 by 2. This will be 1 plus nx and here it is minus 1 by 2 into x minus 0.3 plus n into n minus 1 which means minus 1 by 2 into minus 1 by 2 minus 1 over 1 into 2 into x square that is minus 0.3 whole square plus so on. Now this will be equal to 1 plus minus into minus is plus and it will be 0.3 by 2 plus minus 1 by 2 into minus 1 by 2 minus 1 is minus 3 by 2 over 1 into 2 into minus 0.3 whole square is 0.09 plus so on. Further this will be equal to 1 plus 0.15 plus on calculating this minus into minus will be plus 1 by 2 into 3 by 2 over 1 into 2 will give 3 by 8 into 0.09 plus so on. Now this will be equal to 1 plus 0.15 plus on calculating this it will be 0.3375 plus so on. Now on ending we get it equal to 1.18375. Now this will be equal to on rounding off it will be 1.184 correct to 3 places of decimals. Therefore the value of 1 over root 0.7 is equal to 1.184 correct to 3 places of decimals. So this is the solution of this question and that's all for the session. Hope you all have enjoyed the session.