True or false quiz on rational and irrational numbers with answer options and correction instructions.

Since I can't view or access uploaded images directly, I can’t see the specific content of your image. However, based on the text you've provided, it looks like a math worksheet about rational and irrational numbers with two parts:

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🔍 Understanding Rational and Irrational Numbers:

- Rational Number: A number that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$. This includes:
- Integers (e.g., $-3$, $5$)
- Terminating decimals (e.g., $0.75 = \frac{3}{4}$)
- Repeating decimals (e.g., $0.\overline{3} = \frac{1}{3}$)

- Irrational Number: A number that cannot be written as a fraction of integers. It has a non-repeating, non-terminating decimal. Examples:
- $\sqrt{2}$, $\pi$, $e$

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Let’s go through Part 1 and evaluate each statement.

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✔ Part 1: True or False

#### 1. $12.05$ is a rational number.
- True
→ $12.05 = \frac{1205}{100} = \frac{241}{20}$ → rational

#### 2. $\pi$ is an irrational number.
- True
→ $\pi$ is well-known to be irrational

#### 3. $-2\frac{1}{4}$ is a rational number.
- True
→ $-2\frac{1}{4} = -\frac{9}{4}$ → rational

#### 4. $\sqrt{7}$ is a rational number.
- False
→ $\sqrt{7}$ is irrational (not a perfect square)

#### 5. $\sqrt{17}$ is a rational number.
- False
→ $\sqrt{17}$ is irrational (not a perfect square)

#### 6. $-4.3$ is an irrational number.
- False
→ $-4.3 = -\frac{43}{10}$ → rational

#### 7. $\sqrt{81}$ is a rational number.
- True
→ $\sqrt{81} = 9$ → integer → rational

#### 8. $\frac{2}{3}$ is a rational number.
- True
→ Already a fraction → rational

#### 9. $\sqrt{16} + \sqrt{25}$ is a rational number.
- True
→ $\sqrt{16} = 4$, $\sqrt{25} = 5$, so $4 + 5 = 9$ → rational

#### 10. $\sqrt{6} + \sqrt{4}$ is a rational number.
- False
→ $\sqrt{6}$ is irrational, $\sqrt{4} = 2$ → sum of irrational and rational is irrational
→ So total is irrational

#### 11. $17.55$ is a rational number.
- True
→ $17.55 = \frac{1755}{100} = \frac{351}{20}$ → rational

#### 12. $5\pi + \sqrt{54}$ is an irrational number.
- True
→ $5\pi$ is irrational, $\sqrt{54} = \sqrt{9 \cdot 6} = 3\sqrt{6}$ → also irrational
→ Sum of two irrationals can be irrational (in this case, yes)
→ But even if they were "nice", this expression doesn't simplify to a rational number → remains irrational

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✔ Summary of Part 1 Answers:

| # | Statement | Answer |
|---|---------|--------|
| 1 | $12.05$ is rational | True |
| 2 | $\pi$ is irrational | True |
| 3 | $-2\frac{1}{4}$ is rational | True |
| 4 | $\sqrt{7}$ is rational | False |
| 5 | $\sqrt{17}$ is rational | False |
| 6 | $-4.3$ is irrational | False |
| 7 | $\sqrt{81}$ is rational | True |
| 8 | $\frac{2}{3}$ is rational | True |
| 9 | $\sqrt{16} + \sqrt{25}$ is rational | True |
| 10 | $\sqrt{6} + \sqrt{4}$ is rational | False |
| 11 | $17.55$ is rational | True |
| 12 | $5\pi + \sqrt{54}$ is irrational | True |

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✔ Part 2: Correct the False Statements

We need to change the number in each false statement to make it true, using numbers not used earlier.

#### ✘ Statement 4: $\sqrt{7}$ is a rational number → False
- Change $\sqrt{7}$ to $\sqrt{9} = 3$ → rational
- New statement: $\sqrt{9}$ is a rational number → True

#### ✘ Statement 5: $\sqrt{17}$ is a rational number → False
- Change to $\sqrt{16} = 4$
- New: $\sqrt{16}$ is a rational number → True

#### ✘ Statement 6: $-4.3$ is an irrational number → False
- Change $-4.3$ to $\sqrt{2}$ → irrational
- New: $\sqrt{2}$ is an irrational number → True

#### ✘ Statement 10: $\sqrt{6} + \sqrt{4}$ is a rational number → False
- Change $\sqrt{6}$ to $\sqrt{9} = 3$, so now $3 + 2 = 5$
- New: $\sqrt{9} + \sqrt{4}$ is a rational number → True

> Note: We already used $\sqrt{9}$ in statement 4, but since we're allowed to reuse unless specified otherwise, and the problem says “numbers that have not been used,” we should avoid reusing.

Wait — let's be careful. The instruction says: *"Change the number in each false statement to make the statement true. Be sure to use numbers that have not been used in this problem."*

So far, numbers used include:
- $12.05$, $\pi$, $-2\frac{1}{4}$, $\sqrt{7}$, $\sqrt{17}$, $-4.3$, $\sqrt{81}$, $\frac{2}{3}$, $\sqrt{16}$, $\sqrt{25}$, $17.55$, $5\pi$, $\sqrt{54}$

We must pick new numbers not previously used.

Let’s revise:

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#### ✔ Revised Part 2:

Statement 4: $\sqrt{7}$ is rational → False
→ Change to $\sqrt{4} = 2$ → rational
But $\sqrt{4}$ was used in statement 10? Wait, no — $\sqrt{4}$ appears in statement 10, but we're changing it later.

Wait — in statement 10, we have $\sqrt{6} + \sqrt{4}$, so $\sqrt{4}$ is already used.

So avoid $\sqrt{4}$, $\sqrt{9}$, $\sqrt{16}$, etc.

Let’s pick $\sqrt{25}$? But that's used in statement 9.

Better idea: Use $\sqrt{36}$ → $6$ → rational

So:
- Change $\sqrt{7}$ to $\sqrt{36}$
- New: $\sqrt{36}$ is a rational number → True

✔ Not used before → OK

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Statement 5: $\sqrt{17}$ is rational → False
→ Change to $\sqrt{25} = 5$ → but $\sqrt{25}$ used in #9
→ Try $\sqrt{49} = 7$ → new

New: $\sqrt{49}$ is a rational number → True

✔ $\sqrt{49}$ not used yet → OK

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Statement 6: $-4.3$ is irrational → False
→ Change $-4.3$ to $\sqrt{2}$ → irrational

New: $\sqrt{2}$ is an irrational number → True

✔ $\sqrt{2}$ not used before → OK

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Statement 10: $\sqrt{6} + \sqrt{4}$ is rational → False
→ Change $\sqrt{6}$ to $\sqrt{1}$ → $1$, then $1 + 2 = 3$ → rational

But $\sqrt{1}$ is trivial, and may be considered used implicitly?

Alternatively: change to $\sqrt{0} = 0$, then $0 + 2 = 2$ → rational

But better: use $\sqrt{9}$? Already used.

How about: change to $\sqrt{25}$? Already used.

Try: $\sqrt{81}$? Used in #7.

Use $\sqrt{100} = 10$ → new

So: $\sqrt{100} + \sqrt{4} = 10 + 2 = 12$ → rational

New: $\sqrt{100} + \sqrt{4}$ is a rational number → True

✔ $\sqrt{100}$ not used before → OK

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✔ Final Part 2 Corrections:

| Original False Statement | Correction | New Statement | Reason |
|--------------------------|-----------|----------------|--------|
| 4. $\sqrt{7}$ is rational | Replace $\sqrt{7}$ with $\sqrt{36}$ | $\sqrt{36}$ is a rational number | $\sqrt{36} = 6$ → rational |
| 5. $\sqrt{17}$ is rational | Replace $\sqrt{17}$ with $\sqrt{49}$ | $\sqrt{49}$ is a rational number | $\sqrt{49} = 7$ → rational |
| 6. $-4.3$ is irrational | Replace $-4.3$ with $\sqrt{2}$ | $\sqrt{2}$ is an irrational number | $\sqrt{2}$ is known irrational |
| 10. $\sqrt{6} + \sqrt{4}$ is rational | Replace $\sqrt{6}$ with $\sqrt{100}$ | $\sqrt{100} + \sqrt{4}$ is a rational number | $10 + 2 = 12$ → rational |

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🟩 Final Answer Summary:

#### Part 1: True/False
1. True
2. True
3. True
4. False
5. False
6. False
7. True
8. True
9. True
10. False
11. True
12. True

#### Part 2: Corrected Statements
- 4. $\sqrt{36}$ is a rational number
- 5. $\sqrt{49}$ is a rational number
- 6. $\sqrt{2}$ is an irrational number
- 10. $\sqrt{100} + \sqrt{4}$ is a rational number

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