Square Root of 463
2026-02-28 10:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-463

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 463, we take 63 and 4 as groups.

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

Step 3: Now bring down 63, 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, and we need to find n such that 4n × n ≤ 63. If we consider n as 1, then 41 × 1 = 41.

Step 5: Subtract 63 from 41; the difference is 22, 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 2200.

Step 7: The new divisor is 422. We find n = 5 because 425 × 5 = 2125.

Step 8: Subtracting 2125 from 2200 gives a result of 75.

Step 9: Now the quotient is 21.5.

Step 10: Continue doing these steps until we get two numbers after the decimal point. If needed, continue until the remainder is zero.

So the square root of √463 ≈ 21.5