Finding Square Root by Division Method
This method is an efficient technique to calculate the square root of a number manually. Follow the steps outlined below:
Step 1: Prepare the Number
- Write the number whose square root is to be found.
- Place a bar over every pair of digits starting from the decimal point and moving left. For example, for 152.2756, group it as 1 | 52 | 27 | 56.
Step 2: Find the Largest Square
- Identify the largest perfect square less than or equal to the leftmost group.
- Subtract this square from the leftmost group and write down the result.
Step 3: Double the Quotient
- Write the quotient (the number found in the previous step) below the line.
- Double this quotient and use it as your new divisor.
Step 4: Determine the Next Digit
- Bring down the next pair of digits next to the remainder.
- Find a digit (let's call it x) that can be added to the doubled quotient, forming a new divisor (2Q + x), such that (2Q + x) * x is less than or equal to the new number formed.
Step 5: Repeat the Process
- Subtract the product from the new number to get a new remainder.
- Bring down the next pair of digits, if available, and repeat steps 3-5 until you achieve the desired accuracy.
Example:
- To find √152, group it as 1 | 52.
- The largest square less than 1 is 1 (1²). Subtract to get 0.
- Double the quotient (0) gives 0. Bring down the next pair to work with 52.
- Find the appropriate digit and continue.
This method provides an accurate square root through systematic division and can be used for both whole numbers and decimals.