Square Root of 7956
2026-02-28 11:31 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-7956

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 7956, we need to group it as 56 and 79.

Step 2: Now we need to find n whose square is close to or less than 79. We can say n is ‘8’ because 8 × 8 = 64, which is less than or equal to 79. Now the quotient is 8, and after subtracting 79 - 64, the remainder is 15.

Step 3: Now let us bring down 56, which is the new dividend. Add the old divisor with the same number, 8 + 8 = 16, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 16n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 16n × n ≤ 1556. Let us consider n as 9, now 16 × 9 = 144.

Step 6: Subtract 1556 from 144, and the difference is 1256, and the quotient is 89.

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 125600.

Step 8: Now we need to find a new divisor that is 892 because 892 × 2 = 1784, which is less than 12560.

Step 9: Subtracting 1784 from 12560, we get the result 10776.

Step 10: Now the quotient is 89.1

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 √7956 is approximately 89.1922.