Match the point on the number line best associated with each irrational number:

Question

(4 points)
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91−−√
52−−√
38−−√
59−−√
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Answer 1

To match the points on a number line with the given irrational numbers, we first need to approximate the values of these square roots:

1. \( \sqrt{91} \)

   • \( 9^2 = 81 \) and \( 10^2 = 100 \)
   • So, \( \sqrt{91} \) is between 9 and 10.
   • A more precise approximation would be around 9.54.

2. \( \sqrt{52} \)

   • \( 7^2 = 49 \) and \( 8^2 = 64 \)
   • So, \( \sqrt{52} \) is between 7 and 8.
   • A more precise approximation would be around 7.21.

3. \( \sqrt{38} \)

   • \( 6^2 = 36 \) and \( 7^2 = 49 \)
   • So, \( \sqrt{38} \) is between 6 and 7.
   • A more precise approximation would be around 6.16.

4. \( \sqrt{59} \)

   • \( 7^2 = 49 \) and \( 8^2 = 64 \)
   • So, \( \sqrt{59} \) is between 7 and 8.
   • A more precise approximation would be around 7.68.

Now that we've estimated the square roots, we can summarize their approximate values:

• \( \sqrt{91} \approx 9.54 \)
• \( \sqrt{52} \approx 7.21 \)
• \( \sqrt{38} \approx 6.16 \)
• \( \sqrt{59} \approx 7.68 \)

To match them on a number line:

• Place \( \sqrt{38} \) at approximately 6.16
• Place \( \sqrt{52} \) at approximately 7.21
• Place \( \sqrt{59} \) at approximately 7.68
• Place \( \sqrt{91} \) at approximately 9.54

Find the corresponding points on the number line and place each of the irrational numbers accordingly.