Square Root of 406
2026-02-28 01:09 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-406

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 406, we need to group it as 06 and 4.

Step 2: Now we need to find n whose square is less than or equal to 4. We can say n as ‘2’ because 2 x 2 = 4. Now the quotient is 2, and after subtracting 4 - 4, the remainder is 0.

Step 3: Bring down 06, 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 4n. We need to find the value of n such that 4n x n ≤ 06.

Step 5: Considering n as 1, we get 41 x 1 = 41.

Step 6: Subtract 41 from 60, and the difference is 19. The quotient is 20.

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 1900.

Step 8: We need to find the new divisor. Let us consider n as 4; then 404 x 4 = 1616.

Step 9: Subtracting 1616 from 1900, we get the result 284.

Step 10: Now the quotient is 20.1. Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √406 is approximately 20.12.