Square Root of 1562
2026-02-28 09:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1562

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 1562, we need to group it as 62 and 15.

Step 2: Now we need to find n whose square is 1. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 15. Now, the quotient is 3, and after subtracting 9 from 15, the remainder is 6.

Step 3: Now let us bring down 62, 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 the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 662. Let us consider n as 9, now 69 x 9 = 621.

Step 6: Subtract 662 from 621; the difference is 41, 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 zeroes to the dividend. Now the new dividend is 4100.

Step 8: Now we need to find the new divisor that is 395 because 395 x 9 = 3555.

Step 9: Subtracting 3555 from 4100, we get the result 545.

Step 10: Now the quotient is 39.5.

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 √1562 is approximately 39.52.