Squared Numbers and Square Roots - Free Printable

Let's solve the "Squares and Square Roots" worksheet step by step.

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🔍 Understanding the Task

You are given:

- A grid with numbers (some are perfect squares, some are square roots).
- At the bottom of the page, there is a strip with expressions like:
- $9^2$, $\sqrt{49}$, $6^2$, $\sqrt{16}$, etc.
- Your job: Cut out these expressions and glue them into the correct box next to their equivalent number.

So, for each number in the boxes (like 5, 7, 36, etc.), you need to find which expression from the bottom equals that number.

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✔ Step-by-step Matching

We’ll go through each number in the boxes and match it to its equivalent expression from the bottom.

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#### Left Column:
1. 5 → Look for something that equals 5
- Check: $\sqrt{25} = 5$ → Yes!
➤ Match: $\sqrt{25}$

2. 7 → What gives 7?
- $\sqrt{49} = 7$ → Yes!
➤ Match: $\sqrt{49}$

3. 36 → Is this a square?
- $6^2 = 36$ → Yes!
➤ Match: $6^2$

4. 8 → What gives 8?
- $\sqrt{64} = 8$ → Yes!
➤ Match: $\sqrt{64}$

5. 3 → What gives 3?
- $\sqrt{9} = 3$ → Yes!
➤ Match: $\sqrt{9}$

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#### Middle Column:
1. 81 → What gives 81?
- $9^2 = 81$ → Yes!
➤ Match: $9^2$

2. 25 → What gives 25?
- $5^2 = 25$ → Yes!
➤ Match: $5^2$

3. 9 → What gives 9?
- $3^2 = 9$ → Yes!
➤ Match: $3^2$

4. 4 → What gives 4?
- $2^2 = 4$ → But wait — $2^2$ isn’t listed.
- $\sqrt{16} = 4$ → Yes!
➤ Match: $\sqrt{16}$

5. 11 → What gives 11?
- $\sqrt{121} = 11$ → Yes!
➤ Match: $\sqrt{121}$

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#### Right Column:
1. 10 → What gives 10?
- $\sqrt{100} = 10$ → Yes!
➤ Match: $\sqrt{100}$

2. 64 → What gives 64?
- $8^2 = 64$ → Yes!
➤ Match: $8^2$

3. 6 → What gives 6?
- $\sqrt{36} = 6$ → Yes!
➤ Match: $\sqrt{36}$

4. 49 → What gives 49?
- $7^2 = 49$ → Yes!
➤ Match: $7^2$

5. 12 → What gives 12?
- $\sqrt{144} = 12$ → Yes!
➤ Match: $\sqrt{144}$

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📌 Final Answers (Matching):

| Number | Equivalent Expression |
|--------|------------------------|
| 5 | $\sqrt{25}$ |
| 7 | $\sqrt{49}$ |
| 36 | $6^2$ |
| 8 | $\sqrt{64}$ |
| 3 | $\sqrt{9}$ |
| 81 | $9^2$ |
| 25 | $5^2$ |
| 9 | $3^2$ |
| 4 | $\sqrt{16}$ |
| 11 | $\sqrt{121}$ |
| 10 | $\sqrt{100}$ |
| 64 | $8^2$ |
| 6 | $\sqrt{36}$ |
| 49 | $7^2$ |
| 12 | $\sqrt{144}$ |

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✔ Summary

You would cut out the expressions at the bottom and glue them as follows:

- $\sqrt{25}$ → 5
- $\sqrt{49}$ → 7
- $6^2$ → 36
- $\sqrt{64}$ → 8
- $\sqrt{9}$ → 3
- $9^2$ → 81
- $5^2$ → 25
- $3^2$ → 9
- $\sqrt{16}$ → 4
- $\sqrt{121}$ → 11
- $\sqrt{100}$ → 10
- $8^2$ → 64
- $\sqrt{36}$ → 6
- $7^2$ → 49
- $\sqrt{144}$ → 12

All expressions at the bottom are used exactly once.

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✔ Done! This completes the worksheet. Each number has a matching square or square root expression.