 Hello and welcome to the session. In this session we discussed the following question which says evaluate root 5 correct up to 2 places of decimal. Now let's proceed with the solution. We need to find the square root of the number 5. We will find the square root of 5 by long division method. So for this we will write the number 5 here. Since we need to find this value of square root 5 up to 2 places of decimal, so for this we will find the value of square root 5 up to 3 places of decimal and then rounded off to 2 places of decimal. To start with we write the number 5 here, put a decimal. Now since first we will find the square root 5 up to 3 places of decimal so we will put 6 zeros after the decimal. Now we will make pairs of these digits. This is one pair, this is another pair, this is another pair and this digit 5 is left alone. First you need to think of the largest number whose square is equal to or just less than this number 5. We know that 2 square is equal to 4. This is less than 5. So we will take this number 2 as the divisor and also as the quotient and we know that 2 times is 4. We subtract this square from this number 5. We get 1 and now we put this decimal after 5 in the quotient after the digit 0 and we take down the next pair of digits that is 0 0 with 1. Now we double this quotient 2 so we get 4. We write 4 in this divisor with a blank. In this blank we put a digit which will also be taken as the next digit of the quotient after the decimal and this would be chosen in such a way that the product of the new divisor and the digit in this blank is equal to or just less than the new dividend which is 100. Now we know that 42 2 times is 84 which is less than the new dividend that is 100. So we will put the digit 2 in this blank and this 2 will also be put after the decimal in the quotient. Now this 42 2 times is 84. We subtract 84 from 100 we get 16. We take down this next pair of digits 0 0 along with 16. We double the quotient that is we get 44. We put a blank after 44 and again in the same way we choose the digit to be put in this blank and also in the quotient in such a way that the product of this new divisor and the digit would be less than this new dividend that is 1600. Now 443 3 times is 1329 which is less than the new dividend 1600. So we will put the digit 3 in this blank and also in the quotient after the digit 2. So 443 3 times is 1329. We subtract 1329 from 1600 this gives us 271. Now we take down this last pair of digits left with us 0 0 along with 271. Double the quotient which gives us 446 put a blank after 6. Now 4466 6 times is 26796 which is less than the new dividend 2710. So we will put the digit 6 in this blank and also in the quotient after the digit 3. So here we have 26796 and we subtract this form 271 double 0 which gives us 304. Now since we have used all the pairs of the digits form so we will stop the division here only and this quotient would give us the square root of the number 5. So we get square root of 5 is 2.236. Now square root of 5 is 2.236 up to 3 places of decimal. But we need to find the square root of 5 up to 2 places of decimal. So we round it off to 2 places of decimal. So this would give us square root 5 is equal to 2.24 places of decimal. Hence our final answer is square root 5 is equal to 2.24 correct decimal. It's the session hope you have understood the solution for this question.