Square Root of 340
2026-02-28 09:02 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-340

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 340, we need to group it as 40 and 3.

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

Step 3: Now let us bring down 40, making the new dividend 240. 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 the sum of the dividend and quotient. Now we get 2n as the new divisor. We need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 240. Let us consider n as 8. Now 28 x 8 = 224.

Step 6: Subtract 224 from 240; the difference is 16, and the quotient is 18.

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 1600.

Step 8: Now we need to find the new divisor. We choose 184 because 184 x 4 = 736.

Step 9: Subtracting 736 from 1600, we get the result 864.

Step 10: Now the quotient is 18.4

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

So the square root of √340 is approximately 18.439.