Square Root of 1290
2026-02-28 10:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1290

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 1290, we need to group it as 90 and 12.

Step 2: Now we need to find n whose square is ≤ 12. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 12. Now the quotient is 3, after subtracting 9 from 12, the remainder is 3.

Step 3: Now let us bring down 90, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 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, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 390. Let us consider n as 6, now 66 x 6 = 396, which is too high; try n as 5, then 65 x 5 = 325.

Step 6: Subtract 325 from 390; the difference is 65, 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 6500.

Step 8: Now we need to find the new divisor, which is 709 because 709 x 9 = 6381.

Step 9: Subtracting 6381 from 6500, we get the result 119.

Step 10: Now the quotient is 35.8.

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 √1290 is approximately 35.89.