Square Root of 5700
2026-02-28 11:28 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5700

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 5700, we need to group it as 57 and 00.

Step 2: Now we need to find n whose square is less than or equal to 57. We can say n is ‘7’ because 7 × 7 = 49, which is less than 57. Now the quotient is 7, and after subtracting 49 from 57, the remainder is 8.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 140 as the new partial divisor, and we need to find the value of n.

Step 5: The next step is finding 140n × n ≤ 800. Let us consider n as 5, and now 140 × 5 = 700.

Step 6: Subtract 800 from 700, the difference is 100, and the quotient is 75.

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 10000.

Step 8: Now we need to find the new divisor, which is 150, because 1500 × 6 = 9000.

Step 9: Subtracting 9000 from 10000 gives the result 1000.

Step 10: Now the quotient is 75.49.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero.

So the square root of √5700 is approximately 75.497.