Square Root of 2521
2026-02-28 23:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2521

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 2521, we need to group it as 21 and 25.

Step 2: Now we need to find n whose square is less than or equal to 25. We can say n is ‘5’ because 5 x 5 = 25. Now the quotient is 5, and after subtracting 25 - 25, the remainder is 0.

Step 3: Bring down 21, which is the new dividend. Add the old divisor with the same number 5 + 5 = 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 x n ≤ 21. Let us consider n as 2, now 10 x 2 x 2 = 40, which is greater than 21, so n should be 1.

Step 6: Multiply 10 x 1 = 10, and subtract 21 - 10, the difference is 11, and the quotient is 51.

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 1100.

Step 8: Now, the new divisor becomes 102. Find n such that 102n x n ≤ 1100. We find n = 9 works because 102 x 9 = 918.

Step 9: Subtract 918 from 1100, and we get the result 182.

Step 10: Now, the quotient is 50.9.

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

So the square root of √2521 is approximately 50.21.