Square Root of 239
2026-02-28 00:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-239

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 239, we group it as 39 and 2.

Step 2: Now we need to find a number n whose square is 2 or less. We can say n as ‘1’ because 1 × 1 is less than or equal to 2. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Now let us bring down 39, making the new dividend 139. 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 2n, and we need to find the value of n such that 2n × n ≤ 139. Let us consider n as 6, now 26 × 6 = 156, which is greater than 139, so try n as 5, 25 × 5 = 125.

Step 5: Subtract 125 from 139; the difference is 14, and the quotient is 15.

Step 6: 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 1400.

Step 7: Now we need to find the new divisor that is 310 because 310 × 4 = 1240.

Step 8: Subtracting 1240 from 1400, we get 160.

Step 9: Now the quotient is 15.4.

Step 10: 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 √239 ≈ 15.459.