Square Root of 569
2026-02-21 20:29 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-569

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 569, we need to group it as 69 and 5.

Step 2: Now we need to find n whose square is ≤ 5. We can say n is ‘2’ because 2 x 2 = 4, which is lesser than or equal to 5. Now the quotient is 2. After subtracting 4 from 5, the remainder is 1.

Step 3: Let us bring down 69, making the new dividend 169. Add the old divisor to the same number 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 4n, where we need to find the value of n. Step 5: The next step is finding 4n × n ≤ 169. Let us consider n as 4; now, 44 x 4 = 176, which is too large. Try n as 3, 43 x 3 = 129.

Step 6: Subtract 129 from 169; the difference is 40. The quotient is 23.

Step 7: Since the dividend is less than the divisor, we add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 4000.

Step 8: Find the new divisor, which is 476 because 476 x 8 = 3808. Step 9: Subtracting 3808 from 4000, we get the result 192.

Step 10: Now the quotient is 23.8

Step 11: Continue this process until you get two numbers after the decimal point, unless the remainder becomes zero.

So the square root of √569 is approximately 23.83.