Square Root of 7680
2026-02-28 08:43 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-7680

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 7680, we need to group it as 80 and 76.

Step 2: Now we need to find n whose square is close to 76. We can say n as ‘8’ because 8 x 8 = 64, which is lesser than 76. Now the quotient is 8, after subtracting 76 - 64, the remainder is 12.

Step 3: Now let us bring down 80, which is the new dividend. Add the old divisor with the same number 8 + 8, we get 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 x n ≤ 1280. Let us consider n as 7, now 16 x 7 x 7 = 784.

Step 6: Subtract 1280 from 784, the difference is 496, and the quotient is 87.

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 49600.

Step 8: Now we need to find the new divisor that is 175 because 1755 x 5 = 8775.

Step 9: Subtracting 8775 from 49600, we get the result 40825.

Step 10: Now the quotient is 87.5.

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 √7680 is approximately 87.59.