Square Root of 720
2026-02-28 17:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-720

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 720, we need to group it as 20 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n as '2' because 2 x 2 = 4, which is less than 7. Now the quotient is 2, after subtracting 4 from 7 the remainder is 3.

Step 3: Bring down the next pair, which is 20, making the new dividend 320.

Step 4: Double the current quotient (2), which gets us 4, our new partial divisor.

Step 5: Now we find n such that 4n x n ≤ 320. The correct n is 8, because 48 x 8 = 384, which is more than 320, while 47 x 7 = 329. Thus, n = 7, so 47 x 7 = 329.

Step 6: Subtract 320 from 329, the remainder is 9.

Step 7: Since the remainder 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, making it 900.

Step 8: Now we need to find the new divisor. Doubling the current quotient (27), we get 54.

Step 9: Find n such that 54n x n ≤ 900. The correct n is 1, because 541 x 1 = 541.

Step 10: Subtract 541 from 900, and the remainder is 359.

Step 11: Continue doing these steps until we get two numbers after the decimal point or the remainder is zero.

So the square root of √720 ≈ 26.83.