Square Root of 341
2026-02-28 01:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-341

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 group the numbers from right to left. In the case of 341, we group it as 41 and 3.

Step 2: Now we need to find n whose square is less than or equal to 3. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 3. Now the quotient is 1, and after subtracting 1 from 3, the remainder is 2.

Step 3: Bring down 41, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.

Step 4: The new divisor will be 2, and we need to find 2n x n ≤ 241. Let’s consider n as 8, then 28 x 8 = 224.

Step 5: Subtract 224 from 241, the difference is 17, and the quotient is 18.

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 1700.

Step 7: Now we need to find the new divisor. The new divisor is 369 because 369 x 4 = 1476.

Step 8: Subtract 1476 from 1700, and the remainder is 224.

Step 9: Continue this method until the desired precision is achieved.

So the square root of √341 ≈ 18.47