Square Root of 336
2026-02-28 09:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-336

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 336, we group it as 36 and 3.

Step 2: Now we need to find n whose square is 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 36, 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 current divisor and the quotient. Now we get 2n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 236. Let us consider n as 9, now 29 x 9 = 261.

Step 6: Subtract 236 from 261. Since 261 is greater than 236, we need to consider n as 8. Therefore, 28 x 8 = 224.

Step 7: Subtracting 224 from 236 gives the remainder as 12, and the quotient is 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 1200.

Step 9: Now we need to find the new divisor, which is 369 because 369 x 3 = 1107.

Step 10: Subtracting 1107 from 1200 gives the result 93.

Step 11: Now the quotient is 18.3.

Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.

So the square root of √336 is approximately 18.33.