Square Root of 464
2026-02-28 11:57 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-464

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 464, we need to group it as 64 and 4.

Step 2: Now we need to find n whose square is ≤ 4. We can say n is ‘2’ because 2 x 2 = 4. Now the quotient is 2, and after subtracting 4 from 4, the remainder is 0.

Step 3: Now let us bring down 64, 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.

Step 5: The next step is finding 4n x n ≤ 64. Let us consider n as 1, now 4 x 1 x 1 = 4.

Step 6: Subtract 64 from 4, the difference is 60, and the quotient is 21.

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 6000.

Step 8: Now, we need to find the new digit that makes the divisor 421, because 421 x 14 = 5894.

Step 9: Subtracting 5894 from 6000, we get the result 106.

Step 10: Now the quotient is 21.4.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √464 ≈ 21.54.