Square Root of 414
2026-02-28 11:10 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-414

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 414, we need to group it as 14 and 4.

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

Step 3: Now let us bring down 14, 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, and we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 14. Let us consider n as 3. Now 4 × 3 × 3 = 36, which exceeds 14, so we consider n as 2.

Step 6: Subtract 14 from 8 (4 × 2 × 2), and the difference is 6. 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 zeros to the dividend. Now the new dividend is 600.

Step 8: Now we need to find the new divisor that is close to 600. The best fit is 204 because 204 × 2 = 408. Step 9: Subtracting 408 from 600, we get the result 192.

Step 10: Now the quotient is 20.3.

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

So the square root of √414 is approximately 20.346.