Square Root of 699
2026-02-28 13:46 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-699

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 699, we consider it as 6 and 99.

Step 2: Now we need to find n whose square is closest to 6. We can say n as ‘2’ because 2 x 2 = 4, which is lesser than or equal to 6. Now the quotient is 2, after subtracting 4 from 6, the remainder is 2.

Step 3: Now let us bring down 99, which is the new dividend. Add the old divisor with the same number, 2 + 2, to 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, and we need to find the value of n.

Step 5: The next step is finding 4n x n ≤ 299. Let us consider n as 6, now 46 x 6 = 276.

Step 6: Subtract 276 from 299, the difference is 23, 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 2300.

Step 8: Now we need to find the new divisor, which is 529, because 529 x 4 = 2116.

Step 9: Subtracting 2116 from 2300, we get the result 184.

Step 10: Now the quotient is 26.4

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

So the square root of √699 is approximately 26.44.