Square Root of 364
2026-02-28 12:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-364

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 364, we need to group it as 64 and 3.

Step 2: Now we need to find n whose square is 3. We can say n is ‘1’ because 1 × 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 64, 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 ≤ 264. Let us consider n as 9, now 29 × 9 = 261.

Step 6: Subtract 261 from 264; the difference is 3, and the quotient is 19.

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 300.

Step 8: Now we need to find the new divisor, which is 381, because 381 × 1 = 381.

Step 9: Subtracting 381 from 400 results in 19.

Step 10: Now the quotient is 19.0.

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

So the square root of √364 is approximately 19.08.