Square Root of 4834
2026-02-21 20:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4834

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 4834, we need to group it as 48 and 34.

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

Step 3: Now let us bring down 34, making the new dividend 1234. Add the old divisor with the same number, 6 + 6, to get 12, which becomes the new divisor.

Step 4: The new divisor is 12n, so we need to find the value of n.

Step 5: Find 12n x n ≤ 1234. Let us consider n as 9, now 129 x 9 = 1161.

Step 6: Subtract 1161 from 1234; the difference is 73, 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 7300.

Step 8: Now we need to find the new divisor that is 139 because 1395 x 5 = 6975.

Step 9: Subtracting 6975 from 7300, we get the result 325.

Step 10: Now the quotient is 69.5

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

So the square root of √4834 ≈ 69.54