Square Root of 1922
2026-02-28 10:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1922

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 1922, we need to group it as 22 and 19.

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

Step 3: Now let us bring down 22, which is the new dividend. Add the old divisor with the same number 4 + 4 to 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, and we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 322. Let us consider n as 3, now 83 x 3 = 249.

Step 6: Subtract 249 from 322, and the difference is 73, 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 7300.

Step 8: Now we need to find the new divisor that is 8, because 438 x 8 = 3504.

Step 9: Subtracting 3504 from 7300 gives the result 3796.

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 √1922 is approximately 43.84.