Drag the numbers to the boxes to order them from least to greatest value. $$ \square $$ $$ \square $$ . $$ \square $$ . $$ \square $$ . $$ \square $$ $$ \sqrt{32} $$ 16.1 $$ 4 \sqrt{3} $$ $$ 7 . \overline{3} $$ $$ \sqrt{52} $$

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UpStudy AI · Accepted Answer

Sure, let's arrange the given numbers from least to greatest based on their approximate decimal values.

### Given Numbers:
1. $$ \sqrt{32} $$
2. 16.1
3. $$ 4 \sqrt{3} $$
4. $$ 7.\overline{3} $$ (which is 7.333...)
5. $$ \sqrt{52} $$

### Step-by-Step Evaluation:

1. **$$ \sqrt{32} $$**
   $$
   \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \approx 4 \times 1.4142 \approx 5.6568
   $$

2. **$$ 4 \sqrt{3} $$**
   $$
   \sqrt{3} \approx 1.73205 \
   4 \sqrt{3} \approx 4 \times 1.73205 \approx 6.9282
   $$

3. **$$ \sqrt{52} $$**
   $$
   \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111
   $$

4. **$$ 7.\overline{3} $$**
   $$
   7.\overline{3} = 7.3333...
   $$

5. **16.1**
   $$
   16.1 \text{ (Exact value)}
   $$

### Ordering the Numbers:
Based on the approximate values calculated:

1. **$$ \sqrt{32} $$** ≈ 5.6568
2. **$$ 4 \sqrt{3} $$** ≈ 6.9282
3. **$$ \sqrt{52} $$** ≈ 7.2111
4. **$$ 7.\overline{3} $$** ≈ 7.3333...
5. **16.1** ≈ 16.1

### Final Ordered List:
1. $$ \sqrt{32} $$
2. $$ 4 \sqrt{3} $$
3. $$ \sqrt{52} $$
4. $$ 7.\overline{3} $$
5. 16.1

You can **drag and drop** the numbers into the boxes in the above order, starting with $$ \sqrt{32} $$ as the smallest and ending with **16.1** as the largest.
Drag the numbers in the following order from least to greatest: 1. $$ \sqrt{32} $$ 2. $$ 4 \sqrt{3} $$ 3. $$ \sqrt{52} $$ 4. $$ 7.\overline{3} $$ 5. 16.1

Drag the numbers to the boxes to order them from least to greatest value. \( \square \) \( \square \) . \( \square \) . \( \square \) . \( \square \) \( \sqrt{32} \) 16.1 \( 4 \sqrt{3} \) \( 7 . \overline{3} \) \( \sqrt{52} \)

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