Square Root of 1460
2026-02-28 09:46 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1460

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 1460, we need to group it as 60 and 14.

Step 2: Now we need to find n whose square is 14. We can say n as ‘3’ because 3 × 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 60, making the new dividend 560. Add the old divisor with the same number, 3 + 3, to get 6, which will be part of our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we have 6n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 560. Let us consider n as 9, now 6 × 9 = 54, and 549 is the closest product.

Step 6: Subtract 549 from 560; the difference is 11, and the quotient is 39.

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 zeros to the dividend. Now the new dividend is 1100.

Step 8: Now we need to find the new divisor that is 78, because 789 × 1 = 789.

Step 9: Subtracting 789 from 1100, we get the result 311.

Step 10: Now the quotient is 38.2.

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 √1460 is approximately 38.21.