Square Root of 209
2026-02-28 19:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-209

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 209, we need to group it as 09 and 2.

Step 2: Now we need to find n whose square is less than or equal to 2. We can say n as ‘1’ because 1 × 1 is less than or equal to 2. Now the quotient is 1, and after subtracting 1² from 2, the remainder is 1.

Step 3: Now, let us bring down 09, 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 have 2n as the new divisor; we need to find the value of n.

Step 5: Finding 2n × n ≤ 109, let us consider n as 4. Now 24 × 4 = 96.

Step 6: Subtract 96 from 109; the difference is 13, and the quotient is 14.

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 1300.

Step 8: Now we need to find the new divisor that is 289 because 289 × 4 = 1156.

Step 9: Subtracting 1156 from 1300, we get the result 144. Step 10: Now the quotient is 14.4.

Step 11: Continue these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √209 is approximately 14.46.