Square Root of 689
2026-02-28 10:39 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-689

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 689, we have one group: 689.

Step 2: Now we need to find n whose square is less than or equal to 6. We can say n is '2' because 2 x 2 = 4 is less than 6. Now the quotient is 2 and after subtracting, 6 - 4, the remainder is 2.

Step 3: Bring down 89 which is the new dividend. Add the old divisor with the same number 2 + 2, we get 4 which will be our new divisor.

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

Step 5: The next step is finding 4n x n ≤ 289. Let us consider n as 6, now 46 x 6 = 276.

Step 6: Subtract 289 from 276, the difference is 13, and the quotient is 26.

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 1300.

Step 8: Now we need to find the new divisor that is 525, because 525 x 5 = 2625.

Step 9: Subtracting 2625 from 13000, we get the result 675.

Step 10: Now the quotient is 26.25.

Step 11: Continue doing 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 √689 ≈ 26.25.