Question

Find the square root of 442611.

Answer 1

Hint: To find the square root of 442611, will use the long division method. If after bringing down all the pairs of digit formed to find the square root using long division method, we will put point in the question and then bring the pair of zeroes down after each step and if the number is non-terminating we will stop after 3 to 4 steps of finding the digits after point.

Complete step by step answer:
We will follow the method of long division to find the square root of 442611
We will first place bar over every pair of digits starting from right i.e. $\overline{44}\overline{26}\overline{11}$
Now we will find the largest number whose square is less or equal to the number under the left bar (i.e. 44) and we will take that number as quotient and divisor both.
We can see that square of 6 (i.e. 36) is the largest number. So, we will get:

Now we will get the remainder as (8) and then we will bring the next pair (i.e. 26) down. Now, the new dividend is 826.
We will now double the quotient and enter blank space on its right.
Now, we have to find the largest digit to fill that blank which will also become our new digit of quotient, such that multiplication of new divisor and new quotient is less than or equal to dividend (i.e. 826).
So 6 is the largest possible digit, so we will fill the blank space with 6 and also add 6 to the divisor.

Now, again to fill the blank space, we will follow the same procedure as above. Here, 5 is the largest digit which will fill the blank space and we will also add 5 to 1325.

Now, we can see that we have brought down all the numbers, but the remainder is not zero.
So, we will put point after 665 and bring the pair of zero down and repeat every step as above.

So, the largest digit to fill the blank after 1330_ is 2. So, we will get:

Now, we can see that the remainder is still remaining, so we will again bring down a pair of zeroes.

Now, we can see that 9 is the largest possible digit to fill the blank after 13304. So, we will get:

Now, we can see that, again, the remainder is not zero. So, we have again bring down the pair of zeroes and now 0 is the largest possible digit to fill the blank space, hence, we will get:

Since, we have got three digit after point, so we will stop and our answer will be 665.290

Note: Since, the above solution involves a lot of calculation, students are required to not make any calculation mistakes and students should not get confused about the number of zeroes they have to bring after the point. We will always bring a pair of zeros after the point each time.