Powers and Roots - Opinions Nobody Asked For - Free Printable

Let’s solve each inequality one by one, comparing the expressions on both sides. We’ll simplify where possible and use estimation or known square roots to compare.

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1. √16 + 9 ○ √(16 + 9)

- Left: √16 = 4 → 4 + 9 = 13
- Right: √(25) = 5
- So: 13 > 5 → >

✔ Answer: >

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2. √25 + √5 ○ √30

- Left: √25 = 5; √5 ≈ 2.236 → 5 + 2.236 ≈ 7.236
- Right: √30 ≈ 5.477
- So: 7.236 > 5.477 → >

✔ Answer: >

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3. √160 ○ 12

- √160 = √(16×10) = 4√10 ≈ 4 × 3.162 ≈ 12.648
- 12.648 > 12 → >

✔ Answer: >

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4. √15 + 16 ○ √16 + 16

- Left: √15 ≈ 3.873 → 3.873 + 16 ≈ 19.873
- Right: √16 = 4 → 4 + 16 = 20
- So: 19.873 < 20 → <

✔ Answer: <

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5. 15 ○ √200

- √200 = √(100×2) = 10√2 ≈ 10 × 1.414 ≈ 14.14
- 15 > 14.14 → >

✔ Answer: >

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6. √15 + 17 ○ √16 + 16

- Left: √15 ≈ 3.873 → 3.873 + 17 ≈ 20.873
- Right: √16 = 4 → 4 + 16 = 20
- So: 20.873 > 20 → >

✔ Answer: >

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7. 15 ○ √250

- √250 = √(25×10) = 5√10 ≈ 5 × 3.162 ≈ 15.81
- 15 < 15.81 → <

✔ Answer: <

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8. √15 − 3 ○ √16 − 3

- Left: √15 ≈ 3.873 → 3.873 − 3 ≈ 0.873
- Right: √16 = 4 → 4 − 3 = 1
- So: 0.873 < 1 → <

✔ Answer: <

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9. √20 ○ 5

- √20 = √(4×5) = 2√5 ≈ 2 × 2.236 ≈ 4.472
- 4.472 < 5 → <

✔ Answer: <

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10. √15 − 3 ○ √16 − 4

- Left: √15 ≈ 3.873 → 3.873 − 3 ≈ 0.873
- Right: √16 = 4 → 4 − 4 = 0
- So: 0.873 > 0 → >

✔ Answer: >

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✔ Final Answers (in order):

1. >
2. >
3. >
4. <
5. >
6. >
7. <
8. <
9. <
10. >

You can fill in the circles accordingly!