Square Root of 4805
2026-02-28 17:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4805

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 4805, we need to group it as 05 and 48.

Step 2: Now we need to find n whose square is less than or equal to 48. We can say n is ‘6’ because 6 x 6 = 36 is less than 48. Now the quotient is 6, and after subtracting 36 from 48, the remainder is 12.

Step 3: Now let us bring down 05, making the new dividend 1205. Add the old divisor with the same number 6 + 6, we get 12, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 12n x n ≤ 1205 let us consider n as 9, now 129 x 9 = 1161.

Step 6: Subtract 1161 from 1205, the difference is 44, and the quotient is 69.

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 4400.

Step 8: Now we need to find the new divisor that is 693 because 6933 x 3 = 4159.

Step 9: Subtracting 4159 from 4400, we get the result 241.

Step 10: Now the quotient is 69.3.

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

So the square root of √4805 is approximately 69.33.