Square Root of 345
2026-02-28 23:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-345

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 345, we need to group it as 45 and 3.

Step 2: Now we need to find n whose square is closest 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: Now let us bring down 45, which is the new dividend. Add the old divisor with the same number 1 + 1, we get 2, which will be our new divisor.

Step 4: The new divisor will be 2n, and we need to find the value of n.

Step 5: The next step is finding 2n x n ≤ 245. Let us consider n as 9; now, 29 x 9 = 261.

Step 6: Since 261 is greater than 245, we use n as 8. Now 28 x 8 = 224.

Step 7: Subtract 224 from 245; the difference is 21. The quotient is now 18.

Step 8: 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 2100.

Step 9: Now we need to find the new divisor. We get 369 when 369 x 5 = 1845.

Step 10: Subtracting 1845 from 2100, we get the result 255.

Step 11: Now the quotient is 18.5.

Step 12: Continue doing these steps until we get two numbers after the decimal point.

The square root of √345 ≈ 18.57.