Square Root of 865
2026-02-28 01:24 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-865

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 865, we need to group it as 65 and 8.

Step 2: Now we need to find n whose square is less than or equal to 8. We can say n is 2 because 2 × 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Now let us bring down 65, which makes the new dividend 465. Add the old divisor with the same number, 2 + 2, to get 4, which will be our new divisor.

Step 4: The new divisor is 4n. We need to find n such that 4n × n ≤ 465. Let n be 9; then, 49 × 9 = 441.

Step 5: Subtract 441 from 465; the difference is 24, and the quotient is 29.

Step 6: 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 2400.

Step 7: Now we need to find the new divisor, which is 8 because 298 × 8 = 2384.

Step 8: Subtracting 2384 from 2400, we get the result 16.

Step 9: Now the quotient is 29.4.

Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √865 is approximately 29.41.