Locating √8.3 on a Number Line

To locate √8.3 on a number line, we need to follow a step-by-step process. Here's how you can do it:

Step 1: Understand the Concept of Square Root
Before we begin, it's essential to understand the concept of a square root. The square root of a number (√x) is a value that, when multiplied by itself, gives the original number (x). In this case, we want to find the square root of 8.3.

Step 2: Estimate the Value
To get an approximate idea of where √8.3 falls on the number line, we can estimate its value. Since 8.3 is between 8 and 9, we can estimate that √8.3 lies between √8 and √9.

√8 ≈ 2.83
√9 ≈ 3.00

So, √8.3 is approximately 2.83 to 3.00.

Step 3: Divide the Range
To get a more precise location, we can divide the range between 2.83 and 3.00 into smaller intervals. Let's divide it into ten equal parts.

2.83, 2.84, 2.85, 2.86, 2.87, 2.88, 2.89, 2.90, 2.91, 2.92, 2.93, 2.94, 2.95, 2.96, 2.97, 2.98, 2.99, 3.00

Step 4: Check the Squares
To determine where √8.3 falls within these intervals, we need to check the squares of each number. We know that √8.3 is between √8 and √9, so we need to find the squares of these numbers.

√8 ≈ 2.83 (2.83)^2 = 7.99
√9 ≈ 3.00 (3.00)^2 = 9.00

Step 5: Determine the Interval
Comparing the squares, we can see that 8.3 is closer to 9.00 than 7.99. Therefore, we can conclude that √8.3 is closer to 3.00 than 2.83.

So, on the number line, √8.3 would be closer to 3.00.

Step 6: Mark the Location
Using the number line, mark a point closer to 3.00 to indicate the position of √8.3.

Summary:
To locate √8.3 on a number line:
1. Understand the concept of square root.
2. Estimate the value as approximately between √8 and √9.
3. Divide the range between the estimated values into smaller intervals.
4. Check the squares of each number within the intervals.
5. Determine the interval that √8.3 falls into based on the squares.
6. Mark the location on the number line closer to the appropriate value.

By following these steps, you can locate