Square Root of 1926
2026-02-28 08:28 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1926

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 1926, we need to group it as 26 and 19.

Step 2: Now we need to find n whose square is 19. We can say n as ‘4’ because 4 x 4 = 16 is lesser than or equal to 19. Now the quotient is 4, after subtracting 19 - 16, the remainder is 3.

Step 3: Now let us bring down 26, 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 ≤ 326. Let us consider n as 3, now 83 x 3 = 249.

Step 6: Subtracting 326 from 249, the difference is 77, and the quotient is 43.

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 7700.

Step 8: Now we need to find the new divisor that is 439, because 439 x 9 = 3951.

Step 9: Subtracting 3951 from 7700, we get the result 3749.

Step 10: Now the quotient is 43.8.

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

So the square root of √1926 is approximately 43.88.