Square Root of 421
2026-02-28 09:03 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-421

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 421, we can group it as 21 and 4.

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

Step 3: Now let us bring down 21, 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 the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 21. Let us consider n as 5, now 4 × 5 = 20, and 20 × 5 = 100, which is too large. Adjust n accordingly.

Step 6: Subtract 21 from 20, the difference is 1, and 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 100.

Step 8: Now we need to find the new divisor that is approximately 204, as 204 × 5 = 1020.

Step 9: Adjust and continue the process until sufficient decimal accuracy is achieved.

Step 10: The quotient becomes approximately 20.518.