Square Root of 3796
2026-02-28 01:22 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3796

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 3796, we need to group it as 96 and 37.

Step 2: Now we need to find n whose square is close to 37. We can say n is 6 because 6 * 6 = 36, which is lesser than or equal to 37. Now the quotient is 6, and after subtracting 36 from 37, the remainder is 1.

Step 3: Now let us bring down 96, which makes the new dividend 196. Add the old divisor with the same number, 6 + 6, we get 12, which will be our new divisor.

Step 4: The new divisor is now 12n. We need to find the value of n such that 12n * n ≤ 196. Let us consider n as 1, now 12 * 1 * 1 = 12.

Step 5: Subtract 12 from 196; the difference is 184, and the quotient becomes 61.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 18400.

Step 7: Now we need to find the new digit for the divisor, which is approximately 58, because 1218 * 1 = 1218.

Step 8: Subtracting 1218 from 18400 gives the result 17182.

Step 9: 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 √3796 ≈ 61.583.