Square Root of 1360
2026-02-28 23:14 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1360

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 1360, we need to group it as 60 and 13.

Step 2: Now we need to find n whose square is 13. We can say n as '3' because 3 x 3 is lesser than or equal to 13. Now the quotient is 3; after subtracting 9 from 13, the remainder is 4.

Step 3: Now let us bring down 60, 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 x n ≤ 460. Let us consider n as 7, now 67 x 7 = 469, which is too large, so we use n = 6 instead, 66 x 6 = 396.

Step 6: Subtract 396 from 460; the difference is 64, and the quotient is 36.

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 6400.

Step 8: Now we need to find the new divisor that is 736 because 736 x 8 = 5888.

Step 9: Subtracting 5888 from 6400, we get the result 512.

Step 10: Now the quotient is 36.8

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

So the square root of √1360 is approximately 36.89.