Square Root of 405
2026-02-28 14:07 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-405

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, group the numbers from right to left. In the case of 405, group it as 05 and 4.

Step 2: Find n whose square is less than or equal to 4. We can say n is '2' because 2 x 2 = 4. Now the quotient is 2 and the remainder is 0.

Step 3: Bring down 05, which is the new dividend. Add the old divisor with the same number (2 + 2 = 4), which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 05. Let us consider n as 1, now 4 x 1 x 1 = 4.

Step 5: Subtract 5 from 4, the difference is 1.

Step 6: Since the dividend is less than the divisor, we add a decimal point and bring down two zeros, making the new dividend 100.

Step 7: Find the new divisor, which is 41. Use 41n x n ≤ 100. Let n be 2, then 41 x 2 x 2 = 164, which doesn't fit. Try n = 1, and 41 x 1 x 1 = 41.

Step 8: Subtract 41 from 100, the remainder is 59, and the quotient becomes 20.1.

Step 9: Continue these steps for more precision until you get the desired number of decimal places.

So the square root of √405 ≈ 20.12