Square Root of 22.5
2026-02-28 08:20 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-22.5

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 22.5, we start with 22 and add decimal numbers as needed.

Step 2: Now we need to find n whose square is less than or equal to 22. We can say n as ‘4’ because 4 × 4 = 16, which is less than 22. Now the quotient is 4, and after subtracting 16 from 22, the remainder is 6.

Step 3: Bring down 50 (from adding a decimal point and two zeros, as 22.5 is a decimal number) to make the new dividend 650.

Step 4: The new divisor will be the sum of the old divisor with itself, 4 + 4 = 8, and add a digit to the quotient to estimate the next divisor.

Step 5: Find a digit n such that 8n × n is less than or equal to 650. Let n be 7, then 87 × 7 = 609.

Step 6: Subtract 609 from 650, the difference is 41, and the quotient is 4.7.

Step 7: Since the remainder is not zero, we add another pair of zeros to get 4100.

Step 8: Repeat the process to find the next decimal until the desired precision is reached.

So, the square root of √22.5 ≈ 4.74342.