Square Root of 339
2026-02-28 11:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-339

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 339, we need to group it as 39 and 3.

Step 2: Now we need to find n whose square is less than or equal to 3. We can say n is ‘1’ because 1 x 1 is less than or equal to 3. Now the quotient is 1; after subtracting 1 from 3, the remainder is 2.

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, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 239. Let us consider n as 8, now 28 x 8 = 224

Step 6: Subtract 224 from 239, and the difference is 15. The quotient is 18.

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 1500.

Step 8: Now we need to find the new divisor. Considering 286, because 286 x 6 = 1716 is too large, we try 285 x 5 = 1425.

Step 9: Subtracting 1425 from 1500 gives 75.

Step 10: Now the quotient is 18.4

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 √339 is approximately 18.41.