Square Root of 2940
2026-02-28 21:45 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2940

The long division method is particularly useful 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 2940, we need to group it as 40 and 29.

Step 2: Now we need to find n whose square is close to 29. We can say n is 5 because 5^2 = 25, which is less than or equal to 29. Now the quotient is 5, and after subtracting 25 from 29, the remainder is 4.

Step 3: Now let us bring down 40, which is the new dividend. Add the old divisor with the same number 5 + 5 to 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 × n ≤ 440. Let us consider n as 4, now 10 x 4 x 4 = 160

Step 6: Subtracting 160 from 440, the difference is 280, and the quotient is 54.

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 28000.

Step 8: Now we need to find the new divisor, which is 108, because 108 x 108 = 11664

Step 9: Subtracting 11664 from 28000, we get the result 16336.

Step 10: Now the quotient is 54.2

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal, values continue till the remainder is zero.

So the square root of √2940 ≈ 54.22