Square and Square Root worksheet with multiple-choice questions for practice.

Let's solve each question in the "Square and Square Root" worksheet step by step.

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Understanding Key Concepts:

- Square of a number: Multiply the number by itself.
Example: $ 5^2 = 5 \times 5 = 25 $

- Square root of a number: The value that, when multiplied by itself, gives the original number.
Example: $ \sqrt{49} = 7 $ because $ 7 \times 7 = 49 $

> Note: The square root of a positive number is non-negative (principal root). So $ \sqrt{49} = 7 $, not $ -7 $, unless specified otherwise.

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Now, let’s go through each question:

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(1) The square of 5 is:

$ 5^2 = 5 \times 5 = 25 $
✔ Answer: (B) 25

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(2) The square of 6 is:

$ 6^2 = 6 \times 6 = 36 $
✔ Answer: (B) 36

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(3) The square of 9 is:

$ 9^2 = 9 \times 9 = 81 $
✔ Answer: (A) 81

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(4) The square of 15 is:

$ 15^2 = 15 \times 15 = 225 $
✔ Answer: (D) 225

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(5) The square of 17 is:

$ 17^2 = 17 \times 17 = 289 $
✔ Answer: (C) 289

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(6) The square of 19 is:

$ 19^2 = 19 \times 19 = 361 $
✔ Answer: (B) 361

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(7) The square of 21 is:

$ 21^2 = 21 \times 21 = 441 $
✔ Answer: (C) 441

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(8) The square of 56 is:

$ 56^2 = 56 \times 56 $

Let’s compute:
- $ 50^2 = 2500 $
- $ 6^2 = 36 $
- Cross term: $ 2 \times 50 \times 6 = 600 $
- So, $ (50+6)^2 = 50^2 + 2×50×6 + 6^2 = 2500 + 600 + 36 = 3136 $

✔ Answer: (A) 3136

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(9) The square of 33 is:

$ 33^2 = 33 \times 33 $

Use identity: $ (30+3)^2 = 30^2 + 2×30×3 + 3^2 = 900 + 180 + 9 = 1089 $

✔ Answer: (C) 1089

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(10) The square root of 49 is:

$ \sqrt{49} = 7 $ (since $ 7 \times 7 = 49 $)

Note: Although $ (-7)^2 = 49 $, the principal square root is positive.

✔ Answer: (D) 7

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(11) The square root of 64 is:

$ \sqrt{64} = 8 $ (because $ 8 \times 8 = 64 $)

✔ Answer: (D) 8

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(12) The square root of 81 is:

$ \sqrt{81} = 9 $ (because $ 9 \times 9 = 81 $)

✔ Answer: (C) 9

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✔ Final Answers Summary:

| Q# | Answer |
|----|--------|
| 1 | B |
| 2 | B |
| 3 | A |
| 4 | D |
| 5 | C |
| 6 | B |
| 7 | C |
| 8 | A |
| 9 | C |
| 10 | D |
| 11 | D |
| 12 | C |

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📝 Explanation Recap:

- Squaring a number always results in a non-negative value.
- Square roots are typically taken as positive values unless otherwise stated.
- For perfect squares like 49, 64, 81, you can memorize or factor them.

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