Where is √95 located on a number line?
The Correct Answer and Explanation is :
The correct answer is: 9.74
To locate √95 on a number line, we first need to find its approximate value. We know that:
- (9^2 = 81)
- (10^2 = 100)
Since (95) is between (81) and (100), we can conclude that:
[
9 < \sqrt{95} < 10
]
To get a more precise approximation, we can try some decimal values between (9) and (10):
- (9.5^2 = 90.25) (too low)
- (9.6^2 = 92.16) (still too low)
- (9.7^2 = 94.09) (still too low)
- (9.8^2 = 96.04) (too high)
From this, we can narrow it down to:
[
9.7 < \sqrt{95} < 9.8
]
To refine it further, we can try (9.74):
[
9.74^2 = 94.8276 \quad (\text{still too low})
]
Next, try (9.75):
[
9.75^2 = 95.0625 \quad (\text{too high})
]
So, we can determine that:
[
9.74 < \sqrt{95} < 9.75
]
Thus, we can approximate (\sqrt{95} \approx 9.74).
Now, on a number line, we can represent this by marking points for (9.7\) and (9.8) and placing √95 slightly to the right of (9.74), indicating its approximate location.
When visualizing this on a number line, you would draw a horizontal line and label points, marking (9.7) and (9.8) as reference points. The square root of (95) will be placed just a little to the right of (9.74), illustrating its value relative to those benchmark numbers. This method of estimation is valuable for understanding square roots and their positions on a number line.