Let’s go through each equation one by one to verify if the answers are correct.
We’ll use standard order of operations (PEMDAS/BODMAS):
Parentheses → Exponents/Roots → Multiplication/Division → Addition/Subtraction
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1. 12 + 4 × √9 = 24
√9 = 3
→ 4 × 3 = 12
→ 12 + 12 =
24 ✔ Correct
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2. 12 × √4 − 9 = 15
√4 = 2
→ 12 × 2 = 24
→ 24 − 9 =
15 ✔ Correct
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3. (12 + 4) × √9 = 48
(12 + 4) = 16
√9 = 3
→ 16 × 3 =
48 ✔ Correct
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4. 12 × (√4 − 9) = −84
√4 = 2
→ 2 − 9 = −7
→ 12 × (−7) =
−84 ✔ Correct
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5. 12 + √(4 × 9) = 18
Inside root: 4 × 9 = 36
√36 = 6
→ 12 + 6 =
18 ✔ Correct
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6. 12 − 9 × √4 = −6
√4 = 2
→ 9 × 2 = 18
→ 12 − 18 =
−6 ✔ Correct
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7. √(12 + 4) × 9 = 36
Inside root: 12 + 4 = 16
√16 = 4
→ 4 × 9 =
36 ✔ Correct
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8. 12² − 9 × √4 = 126
12² = 144
√4 = 2 → 9 × 2 = 18
→ 144 − 18 =
126 ✔ Correct
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9. 12 + √4 × 9 = 30
√4 = 2 → 2 × 9 = 18
→ 12 + 18 =
30 ✔ Correct
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10. (12² − 9) × √4 = 270
12² = 144 → 144 − 9 = 135
√4 = 2 → 135 × 2 =
270 ✔ Correct
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11. 12 × √4 + 9 = 33
√4 = 2 → 12 × 2 = 24
→ 24 + 9 =
33 ✔ Correct
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12. 12² − √(9 × 4) = 138
9 × 4 = 36 → √36 = 6
12² = 144
→ 144 − 6 =
138 ✔ Correct
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All equations in the image have been verified and are correctly solved.
Final Answer:
All given equations are mathematically correct as shown in the image.
Parent Tip: Review the logic above to help your child master the concept of operations with roots worksheet.
