Square Root of 1740
2026-02-28 13:22 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1740

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1740, we need to group it as 40 and 17.

Step 2: Now we need to find n whose square is less than or equal to 17. We can say n is ‘4’ because 4 x 4 = 16, which is lesser than or equal to 17. Now the quotient is 4 after subtracting 16 from 17, the remainder is 1.

Step 3: Now let us bring down 40 which is the new dividend. Add the old divisor with the same number 4 + 4, we get 8 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 140. Let us consider n as 1, now 81 x 1 = 81.

Step 6: Subtract 81 from 140. The difference is 59, and the quotient is 41.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 5900.

Step 8: Now we need to find the new divisor that is 416 because 416 x 1 = 416

Step 9: Subtracting 416 from 5900, we get the result 1740.

Step 10: Now the quotient is 41.6

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √1740 is approximately 41.69.