Drag four numbers to the boxes to complete the inequality. $$ 2

Question

Drag four numbers to the boxes to complete the inequality. $$ 2<\square<3<\square<4<\square<5<\square $$ $$ 4 \sqrt{2} $$ $$ \sqrt{8} $$ $$ \sqrt{20} $$ $$ \frac{\sqrt{90}}{3} $$ $$ 5 \sqrt{3} $$

UpStudy AI · Accepted Answer

To complete the inequality $$2<\square<3<\square<4<\square<5<\square$$, we need to determine the approximate values of the given numbers and place them in the correct order.

Let's calculate the approximate values of the numbers provided:

1. **Calculate $$4 \sqrt{2}$$**:
   $$
   4 \sqrt{2} \approx 4 \times 1.414 \approx 5.656
   $$

2. **Calculate $$\sqrt{8}$$**:
   $$
   \sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2} \approx 2 \times 1.414 \approx 2.828
   $$

3. **Calculate $$\sqrt{20}$$**:
   $$
   \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} \approx 2 \times 2.236 \approx 4.472
   $$

4. **Calculate $$\frac{\sqrt{90}}{3}$$**:
   $$
   \sqrt{90} = \sqrt{9 \times 10} = 3 \sqrt{10} \approx 3 \times 3.162 \approx 9.486
   $$
   $$
   \frac{\sqrt{90}}{3} \approx \frac{9.486}{3} \approx 3.162
   $$

5. **Calculate $$5 \sqrt{3}$$**:
   $$
   5 \sqrt{3} \approx 5 \times 1.732 \approx 8.66
   $$

Now we have the approximate values:
- $$4 \sqrt{2} \approx 5.656$$
- $$\sqrt{8} \approx 2.828$$
- $$\sqrt{20} \approx 4.472$$
- $$\frac{\sqrt{90}}{3} \approx 3.162$$
- $$5 \sqrt{3} \approx 8.66$$

Next, we can arrange these values in order:
- $$2 < \sqrt{8} \approx 2.828 < \frac{\sqrt{90}}{3} \approx 3.162 < \sqrt{20} \approx 4.472 < 4 < 4 \sqrt{2} \approx 5.656 < 5 < 5 \sqrt{3} \approx 8.66$$

Now we can fill in the boxes:
$$
2 < \sqrt{8} < 3 < \frac{\sqrt{90}}{3} < 4 < \sqrt{20} < 5 < 4 \sqrt{2}
$$

Thus, the completed inequality is:
$$
2 < \sqrt{8} < 3 < \frac{\sqrt{90}}{3} < 4 < \sqrt{20} < 5 < 4 \sqrt{2}
$$
Fill in the boxes with the numbers in the order: $$ 2 < \sqrt{8} < 3 < \frac{\sqrt{90}}{3} < 4 < \sqrt{20} < 5 < 4 \sqrt{2} $$

Drag four numbers to the boxes to complete the inequality.

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