Square Root of 446
2026-02-28 01:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-446

The long division method is particularly used for non-perfect square numbers. 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 446, we need to group it as 4 and 46.

Step 2: Find a number n whose square is ≤ 4. We can say n is 2 because 2 x 2 is less than or equal to 4. Now the quotient is 2, and after subtracting, the remainder is 0.

Step 3: Bring down the next group, which is 46, making it 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. Find n such that 4n x n ≤ 46. Let us consider n as 1, then 41 x 1 = 41.

Step 5: Subtract 46 from 41, the difference is 5, and the quotient is 21.

Step 6: 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 500.

Step 7: Find the new divisor that is 423 because 421 x 1 = 421.

Step 8: Subtracting 421 from 500 gives 79.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.

So the square root of √446 ≈ 21.12.