Square Root of 693
2026-02-28 15:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-693

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 693, we need to group it as 93 and 6.

Step 2: Now we need to find n whose square is 6. We can say n as ‘2’ because 2 x 2 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 93, 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 × n ≤ 293. Let us consider n as 6, now 46 x 6 = 276.

Step 6: Subtract 276 from 293; the difference is 17, 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 1700.

Step 8: Now we need to find the new divisor, which is 263, because 2637 × 7 = 1849.

Step 9: Subtracting 1849 from 1700, we get a negative result. Adjust n to 6, so 2636 × 6 = 1572.

Step 10: Subtracting 1572 from 1700, we get the result 128.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till the remainder is zero.

So the square root of √693 is approximately 26.324.