Square Root of 4160
2026-02-21 20:56 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4160

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 4160, we need to group it as 60 and 41.

Step 2: Now we need to find n whose square is closest to 41. We can say n as ‘6’ because 6 x 6 is 36, which is lesser than 41. Now the quotient is 6 and after subtracting 36 from 41, the remainder is 5.

Step 3: Now let us bring down 60, which is the new dividend. Add the old divisor with the same number 6 + 6, we get 12, which will be our new divisor.

Step 4: The new divisor is 12n, and we need to find the value of n.

Step 5: The next step is finding 12n × n ≤ 560. Let us consider n as 4, now 12 x 4 = 48, so 48 x 4 = 192.

Step 6: Subtract 192 from 560, the difference is 368, and the quotient is 64.

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 36800.

Step 8: Now we need to find the new divisor. If we assume the next digit in the quotient is 9, we calculate 1289 × 9 = 11601, which is less than 36800.

Step 9: Subtract 11601 from 36800, and we get the result 25199.

Step 10: Now the quotient is 64.9

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 √4160 is approximately 64.49