find the square root of1734489 by long division method.
Long Division Method to find Square Root of 1734489
To find the square root of 1734489 by long division method, we follow the steps given below:
Step 1: Group the digits in pairs
Starting from the right-hand side, we group the given number 1734489 in pairs as shown below:
Step 2: Find the largest number whose square is less than or equal to the first pair
In this step, we find the largest number whose square is less than or equal to the first pair 17. The square of 4 is 16, which is less than 17. Hence, we take 4 as the first digit of the square root.
Step 3: Subtract the product of the digit and the remaining number from the first pair
We multiply the digit obtained in the previous step (4) by 40 (i.e., twice the number obtained by adding the next pair of digits to the right of 17). We get 160. We subtract this from the first pair, i.e., 17 - 16 = 1. We bring down the next pair of digits (34) to the right of 1.
Step 4: Bring down the next pair of digits
We bring down the next pair of digits (48) to the right of the remainder 1. So, we have 148 as the new dividend.
Step 5: Double the digit in the quotient obtained in step 2 and find the largest number that satisfies the condition
We double the digit obtained in step 2 (i.e., 4 x 2 = 8) and obtain 16. We place this below the dividend. We then find the largest number whose square is less than or equal to 148. The square of 3 is 9, which is less than 148. Hence, we take 3 as the next digit of the square root.
Step 6: Subtract the product of the digit and the remaining number from the dividend
We multiply the digit obtained in the previous step (3) by 63 (i.e., twice the number obtained by adding the next pair of digits to the right of 34). We get 189. We subtract this from the dividend, i.e., 148 - 189 = -41. Since the result is negative, we add 100 to the dividend (i.e., 148 + 100 = 248) and consider the next pair of digits (i.e., 89).
Step 7: Bring down the next pair of digits
We bring down the next pair of digits (89) to the right of the remainder -41. So, we have 891 as the new dividend.
Step 8: Double the digit in the quotient obtained in step 5 and find the largest