Square Root of 2014
2026-02-28 10:45 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2014

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 2014, we need to group it as 14 and 20.

Step 2: Now we need to find n whose square is 20. We can say n as '4' because 4 x 4 is lesser than or equal to 20. Now the quotient is 4, after subtracting 16 from 20, the remainder is 4.

Step 3: Now let us bring down 14, which is the new dividend. Add the old divisor with the same number, 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 414. Let us consider n as 5, now 85 x 5 = 425.

Step 6: Since 425 is greater than 414, let's try n as 4, now 84 x 4 = 336.

Step 7: Subtract 336 from 414, the difference is 78, and the quotient is 44.

Step 8: 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 7800.

Step 9: Now we need to find the new divisor. Let's try n as 8, making 448 x 8 = 3584.

Step 10: Subtracting 3584 from 7800, we get the result 4216.

Step 11: 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 √2014 is approximately 44.88.