Square Root of 1920
2026-02-28 13:43 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1920

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 1920, we need to group it as 20 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 × 4 = 16, which is lesser than 19. Now the quotient is 4, and after subtracting 16 from 19, the remainder is 3.

Step 3: Now let us bring down 20, making the new dividend 320. 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 the largest digit n such that 8n × n is less than or equal to 320.

Step 5: Let n be 3, then 83 × 3 = 249.

Step 6: Subtract 249 from 320, the difference is 71, 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 7100.

Step 8: Our new divisor is 866 because 866 × 7 = 6062, which is less than 7100.

Step 9: Subtracting 6062 from 7100 gives us a remainder of 1038.

Step 10: The quotient is now 43.8.

Step 11: Continue doing these steps until we get the desired number of decimal places.

So the square root of √1920 is approximately 43.82.