Square Root of 3.4
2026-02-28 15:49 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3.4

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 the right. In the case of 3.4, we consider it as 3.40.

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 × 1 is lesser than or equal to 3. Now the quotient is 1, after subtracting 3 - 1, the remainder is 2.

Step 3: Now let us bring down 40 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 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 × 8 = 224.

Step 6: Subtract 240 from 224, the difference is 16, and the quotient is 1.8.

Step 7: Since we want more decimal places, we add two zeroes to the dividend. Now the new dividend is 1600.

Step 8: The new divisor will be 36 because 368 × 8 = 2944.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

The square root of √3.4 is approximately 1.843.