Square Root of 18.33
2026-02-28 14:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-18.33

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 18.33, we consider 18 as the integer part and .33 as the decimal part.

Step 2: Now we need to find n whose square is less than or equal to 18. We can say n is ‘4’ because 4 x 4 = 16, which is less than 18. Now the quotient is 4, and the remainder is 2 after subtracting 16 from 18.

Step 3: Now let us bring down .33, making it 233 as the new dividend. Add the old divisor with the same number 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the old divisor and the quotient. Now we get 8n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 233. Let us consider n as 2, now 82 x 2 = 164. Step 6: Subtract 233 from 164; the difference is 69, and the quotient becomes 4.2.

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 zeroes to the dividend. Now the new dividend is 6900.

Step 8: Now we need to find the new divisor that is 84. When 842 x 8 = 6720.

Step 9: Subtracting 6720 from 6900, we get the result 180.

Step 10: Now the quotient is 4.28.

Step 11: Continue doing these steps until we get the desired level of precision after the decimal point.

So the square root of √18.33 is approximately 4.281.