Square Root of 1848
2026-02-28 10:50 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1848

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 1848, we need to group it as 48 and 18.

Step 2: Now we need to find n whose square is less than or equal to 18. We can say n as ‘4’ because 4 x 4 = 16 is less than or equal to 18. Now the quotient is 4. Subtracting 16 from 18, the remainder is 2.

Step 3: Now let us bring down 48, which is the new dividend. Add the old divisor with the same number 4 + 4, we get 8, which will be part of our new divisor.

Step 4: The new divisor will be 8, and we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 248. Let us consider n as 3, now 83 x 3 = 249.

Step 6: Subtract 249 from 248, the difference is 1, 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 100.

Step 8: Now we need to find the new divisor that is 861 because 861 x 1 = 861.

Step 9: Subtracting 861 from 1000, we get the result 139.

Step 10: Now the quotient is 43.9.

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

So the square root of √1848 is approximately 42.98.