Square Root of 1090
2026-02-28 10:23 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1090

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 1090, we need to group it as 90 and 10.

Step 2: Now we need to find n whose square is nearest to 10. We can say n as ‘3’ because 3 x 3 = 9, which is less than or equal to 10. Now the quotient is 3; after subtracting 9 from 10, the remainder is 1.

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

Step 5: The next step is finding 6n x n ≤ 190. Let us consider n as 3: 63 x 3 = 189.

Step 6: Subtract 189 from 190; the difference is 1, and the quotient is 33.

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. Let's try 660 x 1 = 660.

Step 9: Subtracting 660 from 1000, we get the result 340.

Step 10: Now the quotient is 33.0.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Continue until the remainder is zero or until a satisfactory approximation is achieved.

So the square root of √1090 ≈ 33.015.