Square Root of 141
2026-02-28 17:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-141

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 141, we need to group it as 41 and 1.

Step 2: Now we need to find n whose square is 1. We can say n is ‘1’ because 1 x 1 is less than or equal to 1. Now the quotient is 1, and after subtracting 1-1, the remainder is 0.

Step 3: Now let us bring down 41, which is the new dividend. Add the old divisor with the same number 1 + 1; we get 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 41. Let us consider n as 1, now 2 x 1 x 1 = 21

Step 6: Subtract 41 from 21; the difference is 20, and the quotient is 11.

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 2000.

Step 8: Now we need to find the new divisor, that is 109, because 219 x 9 = 1971

Step 9: Subtracting 1971 from 2000, we get the result 29.

Step 10: Now the quotient is 11.9

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

So the square root of √141 is approximately 11.87