Square Root of 2204
2026-02-21 20:25 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2204

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 2204, we need to group it as 04 and 22.

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

Step 3: Now, bring down 04, which is the new dividend. Add the old divisor with the same number: 4 + 4 = 8, which becomes our new divisor.

Step 4: The new divisor is 8x; we need to find the value of x such that 8x x x <= 604. Let x be 7, so 87 x 7 = 609.

Step 5: Subtract 609 from 604, and the difference is -5. Since the remainder is negative, reduce x to 6.

Step 6: 86 x 6 = 516. Subtract 516 from 604, and the difference is 88.

Step 7: Add the decimal point and bring down two zeros to the remainder. Now the new dividend is 8800.

Step 8: The new divisor is 932 (86 with 6 added to it). Find x such that 932x x x <= 8800. Let x be 9, so 932 x 9 = 8388.

Step 9: Subtract 8388 from 8800; the result is 412.

Step 10: The quotient is now 46.9. Continue with these steps until you achieve the desired precision.

So, the square root of √2204 is approximately 46.948.