Square Root of 1924
2026-02-28 11:26 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1924

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 1924, we group it as 24 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, after subtracting 19 - 16, the remainder is 3.

Step 3: Now let us bring down 24, which is the new dividend. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find n such that 8n x n ≤ 324. Let us consider n as 3; now 83 x 3 = 249.

Step 5: Subtract 249 from 324; the difference is 75, and the quotient is 43.

Step 6: 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 7500.

Step 7: Now we need to find the new divisor, which is 876 because 876 x 8 = 7008.

Step 8: Subtracting 7008 from 7500 gives us a remainder of 492.

Step 9: Now the quotient is 43.8.

Step 10: Continue doing these steps until we have two numbers after the decimal point. Continue until the remainder is zero, if possible.

So the square root of √1924 is approximately 43.86.