Question

drag each value to the correct location on the table.

identify whether each cube root or square root lies between 2 and 3, 4 and 5, or 9 and 10.

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$$\begin{tabular}{|c|c|c|} \\hline between 2 and 3 & between 4 and 5 & between 9 and 10 \\\\ \\hline & & \\\\ \\hline \\end{tabular}$$

\\(\sqrt3{101}\\) \\(\sqrt{90}\\) \\(\sqrt3{90}\\) \\(\sqrt3{20}\\) \\(\sqrt{20}\\) \\(\sqrt{7}\\) \\(\sqrt3{800}\\)

Explanation:

Analyze the intervals using perfect powers

Using the Perfect Squares and Perfect Cubes knowledge points

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Evaluate each given radical expression

We test each of the seven given values against our intervals:

• \(\sqrt{7}\): Since \(4 < 7 < 9\), we have \(2 < \sqrt{7} < 3\).
• \(\sqrt[3]{20}\): Since \(8 < 20 < 27\), we have \(2 < \sqrt[3]{20} < 3\).
• \(\sqrt{20}\): Since \(16 < 20 < 25\), we have \(4 < \sqrt{20} < 5\).
• \(\sqrt[3]{90}\): Since \(64 < 90 < 125\), we have \(4 < \sqrt[3]{90} < 5\).
• \(\sqrt{90}\): Since \(81 < 90 < 100\), we have \(9 < \sqrt{90} < 10\).
• \(\sqrt[3]{101}\): Since \(64 < 101 < 125\), we have \(4 < \sqrt[3]{101} < 5\).
• \(\sqrt[3]{800}\): Since \(729 < 800 < 1000\), we have \(9 < \sqrt[3]{800} < 10\).

Answer:

Between 2 and 3	Between 4 and 5	Between 9 and 10
\(\sqrt[3]{20}\)	\(\sqrt[3]{90}\)	\(\sqrt[3]{800}\)
	\(\sqrt[3]{101}\)