Math worksheet titled "Square and Cube Roots - Matching Worksheet" featuring ten problems related to finding square and cube roots, with answer choices listed on the right.

Problem: Solve the worksheet on square roots and cube roots.

The task is to find the correct answers for each problem and match them with the provided options. Let's solve each problem step by step.

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#### 1. Find the two values for ∛343
- The cube root of 343 is the number \( x \) such that \( x^3 = 343 \).
- We know that \( 7^3 = 343 \), so \( \sqrt[3]{343} = 7 \).
- Since cube roots can be positive or negative, the two values are \( 7 \) and \( -7 \).

Answer: \( 7, -7 \)

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#### 2. Find the two values for ∛169
- The cube root of 169 is the number \( x \) such that \( x^3 = 169 \).
- Note that 169 is not a perfect cube, but we can approximate it. However, since the problem asks for exact values, we recognize that 169 is not a perfect cube, so there are no integer solutions.
- If we consider the context of the worksheet, it might be a typo or an error. For now, let's assume the problem is asking for the cube root of a perfect cube (e.g., 125 instead of 169). If it were 125, then \( \sqrt[3]{125} = 5 \), and the two values would be \( 5 \) and \( -5 \).

Assuming the problem meant 125:
Answer: \( 5, -5 \)

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#### 3. Solve for \( x^2 = 81 \)
- We need to find \( x \) such that \( x^2 = 81 \).
- Taking the square root of both sides, we get:
\[
x = \pm \sqrt{81} = \pm 9
\]
- So, the solutions are \( 9 \) and \( -9 \).

Answer: \( 9, -9 \)

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#### 4. Solve for \( y^2 = 25 \)
- We need to find \( y \) such that \( y^2 = 25 \).
- Taking the square root of both sides, we get:
\[
y = \pm \sqrt{25} = \pm 5
\]
- So, the solutions are \( 5 \) and \( -5 \).

Answer: \( 5, -5 \)

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#### 5. Solve for \( z^2 = 64 \)
- We need to find \( z \) such that \( z^2 = 64 \).
- Taking the square root of both sides, we get:
\[
z = \pm \sqrt{64} = \pm 8
\]
- So, the solutions are \( 8 \) and \( -8 \).

Answer: \( 8, -8 \)

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#### 6. Solve: \( P^2 = \frac{36}{16} \)
- Simplify the right-hand side:
\[
\frac{36}{16} = \frac{9}{4}
\]
- We need to find \( P \) such that \( P^2 = \frac{9}{4} \).
- Taking the square root of both sides, we get:
\[
P = \pm \sqrt{\frac{9}{4}} = \pm \frac{3}{2}
\]
- So, the solutions are \( \frac{3}{2} \) and \( -\frac{3}{2} \).

Answer: \( \frac{3}{2}, -\frac{3}{2} \)

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#### 7. Solve: \( Q^2 = \frac{81}{144} \)
- Simplify the right-hand side:
\[
\frac{81}{144} = \frac{9}{16}
\]
- We need to find \( Q \) such that \( Q^2 = \frac{9}{16} \).
- Taking the square root of both sides, we get:
\[
Q = \pm \sqrt{\frac{9}{16}} = \pm \frac{3}{4}
\]
- So, the solutions are \( \frac{3}{4} \) and \( -\frac{3}{4} \).

Answer: \( \frac{3}{4}, -\frac{3}{4} \)

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#### 8. Find the side length of a square whose area is 225 m²
- The area of a square is given by \( \text{side}^2 \).
- Let the side length be \( s \). Then:
\[
s^2 = 225
\]
- Taking the square root of both sides, we get:
\[
s = \sqrt{225} = 15
\]
- Since side lengths are positive, the side length is \( 15 \) meters.

Answer: \( 15 \)

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#### 9. What is the side of a square whose area is 289 m²?
- The area of a square is given by \( \text{side}^2 \).
- Let the side length be \( s \). Then:
\[
s^2 = 289
\]
- Taking the square root of both sides, we get:
\[
s = \sqrt{289} = 17
\]
- Since side lengths are positive, the side length is \( 17 \) meters.

Answer: \( 17 \)

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#### 10. A square has an area of 100 m². What is its side?
- The area of a square is given by \( \text{side}^2 \).
- Let the side length be \( s \). Then:
\[
s^2 = 100
\]
- Taking the square root of both sides, we get:
\[
s = \sqrt{100} = 10
\]
- Since side lengths are positive, the side length is \( 10 \) meters.

Answer: \( 10 \)

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Final Answers:

1. \( 7, -7 \) → a. 7
2. \( 5, -5 \) → b. 17
3. \( 9, -9 \) → c. 10
4. \( 5, -5 \) → d. 15
5. \( 8, -8 \) → e. -5, 5
6. \( \frac{3}{2}, -\frac{3}{2} \) → f. \(\frac{3}{2}\)
7. \( \frac{3}{4}, -\frac{3}{4} \) → g. -13, 13
8. \( 15 \) → h. 8
9. \( 17 \) → i. 9
10. \( 10 \) → j. 5

Matched Answers:

1. a. 7
2. b. 17
3. c. 10
4. d. 15
5. e. -5, 5
6. f. \(\frac{3}{2}\)
7. g. -13, 13
8. h. 8
9. i. 9
10. j. 5

Final Answer:
\[
\boxed{a, b, c, d, e, f, g, h, i, j}
\]