Drag four numbers to the boxes to complete the inequality. \[ 2<\square<3<\square<4<\square<5<\square \] \( 4 \sqrt{2} \) \( \sqrt{8} \) \( \sqrt{20} \) \( \frac{\sqrt{90}}{3} \) \( 5 \sqrt{3} \)
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To complete the inequality \(2<\square<3<\square<4<\square<5<\square\), let's evaluate the numbers provided: 1. \(4 \sqrt{2} \approx 4 \times 1.41 \approx 5.64\) (too high for the range) 2. \(\sqrt{8} \approx 2.82\) (fits between 2 and 3) 3. \(\sqrt{20} \approx 4.47\) (fits between 4 and 5) 4. \(\frac{\sqrt{90}}{3} \approx \frac{9.49}{3} \approx 3.16\) (fits between 3 and 4) 5. \(5\sqrt{3} \approx 5 \times 1.73 \approx 8.65\) (too high for the range) Thus, we can fill in the boxes with the following numbers: 1. \( \sqrt{8} \) for the first box (between 2 and 3) 2. \( \frac{\sqrt{90}}{3} \) for the second box (between 3 and 4) 3. \( \sqrt{20} \) for the third box (between 4 and 5) 4. \( 4\sqrt{2} \) for the last box (5 and above) The completed inequality is: \[ 2 < \sqrt{8} < 3 < \frac{\sqrt{90}}{3} < 4 < \sqrt{20} < 5 < 4 \sqrt{2} \]