Square Root of 139
2026-02-28 10:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-139

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 139, we need to group it as 39 and 1.

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

Step 3: Now let us bring down 39, which is the new dividend. Add the old divisor with the same number 1 + 1 to 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, we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 39. Let us consider n as 1, now 2 × 1 × 1 = 2

Step 6: Subtracting 39 from 2 gives the difference of 37, 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 3700.

Step 8: Now we need to find the new divisor, which is 119 because 219 × 9 = 1971.

Step 9: Subtracting 1971 from 3700, we get the result 1729.

Step 10: Now the quotient is 11.9

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

So the square root of √139 is approximately 11.79.