Square Root of 2260
2026-02-28 13:47 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2260

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 2260, we need to group it as 60 and 22.

Step 2: Now, we need to find n whose square is 22. We can say n as ‘4’ because 4 x 4 = 16, which is less than 22. Now the quotient is 4, and after subtracting 16 from 22, the remainder is 6.

Step 3: Now let us bring down 60, making the new dividend 660. Add the old divisor with the same number, 4 + 4, to get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 660. Let's consider n as 7, so 87 x 7 = 609.

Step 6: Subtract 609 from 660; the difference is 51, and the quotient is 47.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal allows us to add two zeros to the dividend. Now the new dividend is 5100.

Step 8: Now we need to find the new divisor, 945, because 945 x 5 = 4725.

Step 9: Subtracting 4725 from 5100 gives us 375.

Step 10: Now the quotient is 47.5.

Step 11: 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 √2260 ≈ 47.55.