Square Root of 3800
2026-02-28 11:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3800

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 3800, we need to group it as 38 and 00.

Step 2: Now we need to find n whose square is 36. We can say n as ‘6’ because 6 × 6 is lesser than or equal to 38. Now the quotient is 6, after subtracting 36 from 38, the remainder is 2.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 6 + 6, we get 12, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 12n × n ≤ 200; let us consider n as 1, now 12 × 1 = 12.

Step 6: Subtract 12 from 200, the difference is 188, and the quotient is 61.

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 18800.

Step 8: Now we need to find the new divisor, which is 123 because 123 × 3 = 369.

Step 9: Subtracting 369 from 18800, we get the result 18431.

Step 10: Now the quotient is 61.3.

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 √3800 is 61.64.