Question

workbook 1a

1. fill the blanks in the following chart.

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$$\begin{tabular}{|c|c|c|} \\hline \\textbf{entire radical} & \\textbf{show all steps} & \\textbf{mixed radical} \\\\ \\hline \\sqrt{150} & & \\\\ \\hline \\sqrt{1029} & & \\\\ \\hline & & 4\\sqrt{5} \\\\ \\hline & & 4\\sqrt{3} \\\\ \\hline \\end{tabular}$$

Explanation:

Identify the task

We need to fill in the missing cells of the table, converting between entire radicals and mixed radicals.

Simplify the first entire radical

We simplify \(\sqrt{150}\) by finding the largest perfect square factor of 150.

$$ 150 = 25 \times 6 $$

$$ \sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6} $$

Simplify the second entire radical

We simplify \(\sqrt{1029}\) by finding the largest perfect square factor of 1029.

$$ 1029 = 49 \times 21 $$

$$ \sqrt{1029} = \sqrt{49 \times 21} = \sqrt{49} \times \sqrt{21} = 7\sqrt{21} $$

Convert the first mixed radical to an entire radical

We convert \(4\sqrt{5}\) to an entire radical by moving the coefficient inside the square root.

$$ 4\sqrt{5} = \sqrt{4^2 \times 5} = \sqrt{16 \times 5} = \sqrt{80} $$

Convert the second mixed radical to an entire radical

We convert \(4\sqrt{3}\) to an entire radical by moving the coefficient inside the square root.

$$ 4\sqrt{3} = \sqrt{4^2 \times 3} = \sqrt{16 \times 3} = \sqrt{48} $$

Answer:

Entire Radical	Show all steps	Mixed Radical
\(\sqrt{1029}\)	\(\sqrt{49 \times 21} = 7\sqrt{21}\)	\(7\sqrt{21}\)
\(\sqrt{80}\)	\(4\sqrt{5} = \sqrt{16 \times 5} = \sqrt{80}\)	\(4\sqrt{5}\)
\(\sqrt{48}\)	\(4\sqrt{3} = \sqrt{16 \times 3} = \sqrt{48}\)	\(4\sqrt{3}\)