Square Root of 2465
2026-02-28 11:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2465

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 2465, we need to group it as 65 and 24.

Step 2: Now we need to find n whose square is 24. We can say n as ‘4’ because 4 x 4 is lesser than or equal to 24. Now the quotient is 4, and after subtracting 24 - 16, the remainder is 8.

Step 3: Now let us bring down 65, which is the new dividend. Add the old divisor with the same number 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 865. Let us consider n as 9, now 89 x 9 = 801.

Step 6: Subtract 865 - 801, the difference is 64, and the quotient is 49.

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 6400.

Step 8: Now we need to find the new divisor that is 993 because 993 x 6 = 5958.

Step 9: Subtracting 5958 from 6400, we get the result 442.

Step 10: Now the quotient is 49.6.

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 √2465 is approximately 49.65.