Square Root of 6076
2026-02-28 19:18 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-6076

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 6076, we need to group it as 76 and 60.

Step 2: Now we need to find n whose square is less than or equal to 60. We can say n as '7' because 7 x 7 = 49, which is less than 60. Now the quotient is 7, and after subtracting 49 from 60, the remainder is 11.

Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number 7 + 7 to get 14, which will be our new divisor.

Step 4: The new divisor will be 14n, where we need to find the value of n such that 14n x n is less than or equal to 1176.

Step 5: Let us consider n as 8. Now 148 x 8 = 1184, which is greater than 1176. Trying n as 7, 147 x 7 = 1029, which is less than 1176.

Step 6: Subtract 1029 from 1176, the difference is 147, and the quotient is 77.

Step 7: Since the dividend is less than the new divisor, we need to add a decimal point. Adding the decimal point allows us to append two zeroes to the dividend. The new dividend is 14700.

Step 8: Now we need to find the new divisor by doubling the previous quotient, 154, and find n such that 1540n x n ≤ 14700. The number n is found to be 9 as 1549 x 9 = 13941.

Step 9: Subtracting 13941 from 14700, we get the result 759.

Step 10: Now the quotient is 77.9.

Step 11: Continue doing these steps until we get the desired number of decimal places. So the square root of √6076 is approximately 77.972.