Q5: The area of the square field is 234.09 m2. The perimeter of the fi...
Understanding the Division Method for Square Roots
The square root of a number can be calculated using the division method. Here is how to calculate √234.09 step by step.
Step 1: Prepare the Number
- Group the digits of the number from right to left into pairs.
- For 234.09, we group it as 2 | 34 | 09.
Step 2: Find the Largest Square
- Identify the largest square number less than or equal to the first group (2).
- The largest square is 1 (since 1 × 1 = 1).
- Write 1 above the line and subtract 1 from 2, leaving 1.
Step 3: Bring Down the Next Pair
- Bring down the next pair (34) next to the remainder (1), making it 134.
Step 4: Double the Quotient
- Double the current quotient (1), giving you 2.
- Think of a number that, when combined with 2 and multiplied by itself, is less than or equal to 134.
Step 5: Find the Next Digit
- Trying 6: (26 × 6 = 156, too high) and 5: (25 × 5 = 125, fits).
- Write 5 above the line next to the 1, making it 15.
- Subtract 125 from 134, leaving 9.
Step 6: Bring Down the Next Pair
- Bring down the next pair (09), making it 909.
Step 7: Repeat the Process
- Double the quotient (15), giving you 30.
- Find the digit (2): (302 × 2 = 604).
- Write 2 above the line, subtracting 604 from 909, leaving 305.
Final Result
- Your result so far is 15.2, with a remainder that can be further calculated if desired.
- Thus, √234.09 ≈ 15.2 using the division method.
This method provides an accurate way to find square roots without a calculator!
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