Question

1. match each point on the number line to one number in the table below. not all numbers are represented on the number line. (3 points) \\(\sqrt{17}\\) \\(\sqrt{0.81}\\) \\(\sqrt{\frac{49}{4}}\\) \\(\sqrt{\frac{1}{9}}\\) \\(\sqrt{24}\\) \\(\sqrt{34}\\) \\(\sqrt{1.21}\\) \\(\sqrt{\frac{81}{16}}\\)

Answer:

To solve this, we first simplify each square root:

• $\boldsymbol{\sqrt{17}} \approx 4.123$ (between 4 and 5)
• $\boldsymbol{\sqrt{0.81}} = 0.9$ (close to 1, left of 1)
• $\boldsymbol{\sqrt{\frac{49}{4}}} = \frac{7}{2} = 3.5$ (between 3 and 4)
• $\boldsymbol{\sqrt{\frac{1}{9}}} = \frac{1}{3} \approx 0.333$ (close to 0, right of 0)
• $\boldsymbol{\sqrt{24}} \approx 4.899$ (between 4 and 5, closer to 5)
• $\boldsymbol{\sqrt{34}} \approx 5.831$ (close to 6)
• $\boldsymbol{\sqrt{1.21}} = 1.1$ (close to 1, right of 1)
• $\boldsymbol{\sqrt{\frac{81}{16}}} = \frac{9}{4} = 2.25$ (between 2 and 3)

Now match to the number line points:

• Point F (close to 0): $\boldsymbol{\sqrt{\frac{1}{9}}}$ (≈0.333)
• Point B (close to 1, left of 1): $\boldsymbol{\sqrt{0.81}}$ (0.9)
• Point A (between 2 and 3): $\boldsymbol{\sqrt{\frac{81}{16}}}$ (2.25)
• Point C (between 3 and 4): $\boldsymbol{\sqrt{\frac{49}{4}}}$ (3.5)
• Point E (at 4): Wait, E is at 4? Wait, no—wait, E is on 4? Wait, the number line: F (0 -1), B (near 1), A (2 -3), C (3 -4), E (at 4), D (near 6). Wait, $\sqrt{17} \approx 4.123$ (so E? Wait, E is at 4, but $\sqrt{17} \approx 4.123$ is just right of 4. Wait, maybe:
• Point E (right of 4): $\boldsymbol{\sqrt{17}}$ (≈4.123)
• Point D (near 6): $\boldsymbol{\sqrt{34}}$ (≈5.831)
• Point C (3 -4): $\boldsymbol{\sqrt{\frac{49}{4}}}$ (3.5)
• Point A (2 -3): $\boldsymbol{\sqrt{\frac{81}{16}}}$ (2.25)
• Point B (near 1, right of 1): $\boldsymbol{\sqrt{1.21}}$ (1.1)
• Point F (near 0): $\boldsymbol{\sqrt{\frac{1}{9}}}$ (≈0.333)
• Point E (at 4, right of 4): $\boldsymbol{\sqrt{17}}$ (≈4.123)
• Point D (near 6): $\boldsymbol{\sqrt{34}}$ (≈5.831)
• Point C (3 -4): $\boldsymbol{\sqrt{\frac{49}{4}}}$ (3.5)
• Point A (2 -3): $\boldsymbol{\sqrt{\frac{81}{16}}}$ (2.25)
• Point B (near 1, left of 1): $\boldsymbol{\sqrt{0.81}}$ (0.9)
• Point F (near 0): $\boldsymbol{\sqrt{\frac{1}{9}}}$ (≈0.333)

Wait, let’s recheck:

• F: closest to 0 → $\sqrt{\frac{1}{9}}$ (≈0.333)
• B: near 1, left of 1 → $\sqrt{0.81}$ (0.9)
• A: between 2 and 3 → $\sqrt{\frac{81}{16}}$ (2.25)
• C: between 3 and 4 → $\sqrt{\frac{49}{4}}$ (3.5)
• E: at 4, but $\sqrt{17} \approx 4.123$ (so E is at 4, but $\sqrt{17}$ is just right of 4 → E: $\sqrt{17}$
• D: near 6 → $\sqrt{34}$ (≈5.831)
• Wait, $\sqrt{24} \approx 4.899$ (between 4 and 5, closer to 5) → so maybe E is $\sqrt{17}$ (≈4.123) and $\sqrt{24}$ (≈4.899) is between E and D? Wait, the number line: E is at 4, then next is 5, then D at 6. So:
• E: $\sqrt{17}$ (≈4.123, right of 4)
• Between E and D (4 -5): $\sqrt{24}$ (≈4.899)
• D: $\sqrt{34}$ (≈5.831, near 6)

Let’s correct:

• F: $\sqrt{\frac{1}{9}}$ (≈0.333)
• B: $\sqrt{0.81}$ (0.9)
• A: $\sqrt{\frac{81}{16}}$ (2.25)
• C: $\sqrt{\frac{49}{4}}$ (3.5)
• E: $\sqrt{17}$ (≈4.123)
• D: $\sqrt{34}$ (≈5.831)
• Wait, what about $\sqrt{1.21}$ (1.1)? Oh, Point B is near 1, left of 1 (0.9), and $\sqrt{1.21}$ (1.1) is right of 1. Wait, the number line: B is at the dot near 1 (before 1? Wait, the number line shows B at the dot before 1? Wait, the number line: 0 --- F --- B --- 1 --- 2 --- A --- 3 --- C --- 4 --- E --- 5 --- D --- 6. So B is between 0 and 1, near 1? Wait, $\sqrt{0.81}=0.9$ (left of 1), $\sqrt{1.21}=1.1$ (right of 1). So:
• F: $\sqrt{\frac{1}{9}}$ (≈0.333)
• B: $\sqrt{0.81}$ (0.9) (left of 1)
• Then between B and 1: maybe $\sqrt{1.21}$ (1.1) is right of 1, but the number line has B at the dot before 1, then 1, then 2. Wait, maybe the problem’s table has 8 numbers, and 6 points? Wait, the problem says “match each point” (F, B, A, C, E, D: 6 points) to “one number in the table” (8 numbers). So we pick 6 numbers.

Final matches (most logical):

• F: $\boldsymbol{\sqrt{\frac{1}{9}}}$ (≈0.333, closest to 0)
• B: $\boldsymbol{\sqrt{0.81}}$ (0.9, close to 1, left of 1)
• A: $\boldsymbol{\sqrt{\frac{81}{16}}}$ (2.25, between 2 and 3)
• C: $\boldsymbol{\sqrt{\frac{49}{4}}}$ (3.5, between 3 and 4)
• E: $\boldsymbol{\sqrt{17}}$ (≈4.123, right of 4)
• D: $\boldsymbol{\sqrt{34}}$ (≈5.831, close to 6)

(Note: $\sqrt{1.21}=1.1$ and $\sqrt{24}≈4.899$ are extra, as we only need 6 matches.)