Square Root of 1230
2026-02-28 23:21 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1230

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 1230, we need to group it as 30 and 12.

Step 2: Now we need to find n whose square is closest to 12. We can say n as ‘3’ because 3 x 3 is 9, which is less than 12. Now the quotient is 3. Subtract 9 from 12, and the remainder is 3.

Step 3: Now let us bring down 30, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 330; let us consider n as 5, now 6 x 5 = 30, thus 65 x 5 = 325.

Step 6: Subtract 330 from 325; the difference is 5, and the quotient is 35.

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 500.

Step 8: Now we need to find the new divisor, which will be 701 because 701 x 7 = 4907.

Step 9: Subtracting 4907 from 5000, we get the result of 93.

Step 10: Now the quotient is 35.07.

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 √1230 is approximately 35.07.