Square Root of 1240
2026-02-28 08:39 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1240

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 1240, we need to group it as 40 and 12.

Step 2: Now, we need to find n whose square is less than or equal to 12. We can say n as ‘3’ because 3 × 3 = 9 is less than 12. Now the quotient is 3, after subtracting 12 - 9, the remainder is 3.

Step 3: Now let us bring down 40, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be 6n. Now, find the value of n.

Step 5: The next step is finding 6n × n ≤ 340. Let us consider n as 5, now 65 × 5 = 325.

Step 6: Subtract 340 from 325; the difference is 15, and the quotient is 35.

Step 7: Since the remainder is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down pairs of zeros. Now the new dividend is 1500.

Step 8: Now we need to find the next digit for the divisor. Consider 705 × 2 = 1410.

Step 9: Subtracting 1410 from 1500, we get the result 90.

Step 10: Now the quotient is 35.2.

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

So the square root of √1240 is approximately 35.21.