This resource helps students practice simplifying radicals by solving 12 problems to reveal a colorful mandala design.

Since the user has not specified any of the options (ExplainAnswer, TeachTopic, GeneratePractice) as true, and only requested to solve the problem accurately, I will proceed by solving the math problems shown in the worksheet.

The worksheet contains 12 problems on simplifying radical expressions. I will solve each one step by step.

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Problem 1: √(16x⁴)
√16 = 4
√x⁴ = x²
→ 4x²

Problem 2: √(49m⁶)
√49 = 7
√m⁶ = m³
→ 7m³

Problem 3: √(216a³)
Factor 216: 216 = 36 × 6 = 6² × 6
So √(216a³) = √(6² × 6 × a² × a) = 6a√(6a)
→ 6a√(6a)

Problem 4: 4√25
√25 = 5
4 × 5 = 20
→ 20

Problem 5: √(81x⁴)
√81 = 9
√x⁴ = x²
→ 9x²

Problem 6: √(5x²)
√x² = x
So √(5x²) = x√5
→ x√5

Problem 7: √(144y⁶)
√144 = 12
√y⁶ = y³
→ 12y³

Problem 8: √(72x³)
72 = 36 × 2 → √72 = 6√2
x³ = x² × x → √x³ = x√x
So √(72x³) = 6x√(2x)
→ 6x√(2x)

Problem 9: -8√(16)
√16 = 4
-8 × 4 = -32
→ -32

Problem 10: -√(28x⁴y²)
28 = 4 × 7 → √28 = 2√7
x⁴ → √x⁴ = x²
y² → √y² = y
So √(28x⁴y²) = 2x²y√7
With the negative sign: → -2x²y√7

Problem 11: √(256x⁸y⁴)
√256 = 16
√x⁸ = x⁴
√y⁴ = y²
→ 16x⁴y²

Problem 12: √(625x¹⁰y⁶)
√625 = 25
√x¹⁰ = x⁵
√y⁶ = y³
→ 25x⁵y³

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Final Answer:
1. 4x²
2. 7m³
3. 6a√(6a)
4. 20
5. 9x²
6. x√5
7. 12y³
8. 6x√(2x)
9. -32
10. -2x²y√7
11. 16x⁴y²
12. 25x⁵y³