Square Root of 801
2026-02-28 08:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-801

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 801, we need to group it as 01 and 8.

Step 2: Now we need to find a number n whose square is less than or equal to 8. We choose n = 2 because 2 x 2 = 4, which is less than 8. The quotient is 2, and the remainder is 4 after subtracting 4 from 8.

Step 3: Bring down the next pair, which is 01, making the new dividend 401.

Step 4: Double the quotient (2), giving us 4, and use it to find a new divisor. Consider 4n as the new divisor, and find n such that 4n x n ≤ 401.

Step 5: By trial, we find that n = 7 works, since 47 x 7 = 329.

Step 6: Subtract 329 from 401 to get a remainder of 72, and the quotient becomes 27.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding a decimal point allows us to add two zeroes to the dividend, making it 7200.

Step 8: Find a new divisor by considering 54 (double the new quotient 27) and find n such that 54n x n ≤ 7200. With n = 1, 541 x 1 = 541.

Step 9: Subtract 541 from 7200 to get a remainder of 6659.

Step 10: The quotient is now approximately 28.301. Continue with these steps until you get the desired precision.

So the square root of √801 ≈ 28.3019.