 Hello and welcome to the session. Today I will help you with the following question. The question says find the square root of the following number by the prime factorization method and the number given to us is 4096. Now let's move on to the solution. Now the number is 4096 and as you can see that the number is an even number so we will start dividing this number by 2. So 4096 when divided by 2 gives us 2048. Now the prime factor for 2048 is also 2. So when this number is divided by 2 we get 1024. Now 1024 when divided by 2 gives us 512. Now 512 is also divisible by 2. So on dividing this number by 2 we get 256. 256 is also divisible by 2 so when 256 divided by 2 we will get 128. Now 128 when divided by 2 gives us 64. 64 when divided by 2 gives us 32. 32 when divided by 2 gives us 16. Now prime factor for 16 is also 2 so when this is divided by 2 we will get 8. 8 when divided by 2 gives us 4. 4 when divided by 2 gives us 2. Now 2 when divided by 2 gives us 1. So we will stop here. So these are the prime factors for the given number. Now prime factorization of 4096 is given by 2 multiplied to itself 12 times. So we get this. Now we will pair up these prime factors. This is one pair. This is the other pair. Third pair. The fourth pair. Fifth pair. And the sixth pair. Now square root of 4096 is given by taking out one factor out of each pair. So from the first pair we have a 2. From the second pair another 2. From the third pair a 2 again. From the fourth pair a 2. From the fifth pair also a 2. And from the last pair also we have a 2. So square root of 4096 is equal to 2 multiplied to itself 6 times. And this is equal to 64. So square root of 4096 is equal to 64. Hence our final answer is 64. So hope you enjoyed this session. Have a good day.