Square Root of 436
2026-02-28 10:23 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-436

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 436, we need to group it as 36 and 4.

Step 2: Now we need to find n whose square is ≤ 4. We can say n as ‘2’ because 2 x 2 is lesser than or equal to 4. Now the quotient is 2; after subtracting 4 - 4, the remainder is 0.

Step 3: Now let us bring down 36, which is the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 4n x n ≤ 36. Let us consider n as 0, now 40 x 0 = 0.

Step 6: Subtract 36 from 0, the difference is 36, and the quotient is 20.

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 3600.

Step 8: Now we need to find the new divisor that is 9 because 409 x 9 = 3681.

Step 9: Subtracting 3681 from 3600 we get the result -81, so we take the next closest number which gives a positive remainder.

Step 10: Now the quotient is 20.8.

Step 11: 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.

So the square root of √436 is approximately 20.88.