Square Root of 574
2026-02-28 18:03 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-574

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 574, we need to group it as 74 and 5.

Step 2: Now we need to find n whose square is less than or equal to 5. We can say n as '2' because 2^2 = 4 is less than 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 74, which is the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 174. Let us consider n as 4, now 44 x 4 = 176.

Step 6: Since 176 is greater than 174, we try n = 3, then 43 x 3 = 129.

Step 7: Subtract 129 from 174, the difference is 45, and the quotient is 23.

Step 8: Since the dividend is greater than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4500.

Step 9: Now we need to find the new divisor that is 239 because 2399 x 9 = 4311. Step 10: Subtracting 4311 from 4500, we get the result 189.

Step 11: The quotient is now 23.9. 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 √574 is approximately 23.96.