Square Root of 3050
2026-02-28 13:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3050

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 3050, we need to group it as 50 and 30.

Step 2: Now we need to find n whose square is 30. We can say n as ‘5’ because \(5 \times 5 = 25\), which is lesser than 30. Now the quotient is 5, after subtracting \(30-25\) the remainder is 5.

Step 3: Now let us bring down 50 which is the new dividend. Add the old divisor with the same number 5 + 5 we get 10, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor, we need to find the value of n.

Step 5: The next step is finding \(10n \times n \leq 550\). Let's consider n as 5, now \(10 \times 5 \times 5 = 250\).

Step 6: Subtract 550 from 250, the difference is 300, and the quotient is 55.

Step 7: Since the dividend is greater 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 30000.

Step 8: Now we need to find the new divisor that is 110 because \(110 \times 2 = 220\).

Step 9: Subtracting 220 from 30000, we get the result 29800.

Step 10: Now the quotient is 55.2.

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 √3050 is 55.22.