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Lesson

Practice Problems

Simplify

\(\textbf{1)}\) \( \sqrt{24} \)

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The answer is \( 2\sqrt{6} \)

\(\textbf{2)}\) \( \sqrt{48} \)

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The answer is \( 4\sqrt{3} \)

\(\textbf{3)}\) \( \sqrt{120} \)

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The answer is \( 2\sqrt{30} \)

\(\textbf{4)}\) \( \sqrt{32} \)

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The answer is \( 4\sqrt{2} \)

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\(\,\,\,\,\,\, \sqrt{32} \)

\(\,\,\,\,\,\, \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2} \)

\(\,\,\,\,\,\, \sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2} \)

\(\,\,\,\,\,\, \sqrt{4 \cdot 4 \cdot 2} \)

\(\,\,\,\,\,\, \sqrt{4} \cdot \sqrt{4} \cdot \sqrt{2} \)

\(\,\,\,\,\,\, 2 \cdot 2 \cdot \sqrt{2} \)

\(\,\,\,\,\,\,\)The answer is \( 4\sqrt{2} \)

\(\textbf{5)}\) \( \sqrt{180} \)

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The answer is \( 6\sqrt{5} \)

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\(\,\,\,\,\,\, \sqrt{180} \)

\(\,\,\,\,\,\, \sqrt{2 \cdot 2 \cdot 3 \cdot 3 \cdot 5} \)

\(\,\,\,\,\,\, \sqrt{(2 \cdot 2) \cdot (3 \cdot 3) \cdot 5} \)

\(\,\,\,\,\,\, \sqrt{4 \cdot 9 \cdot 5} \)

\(\,\,\,\,\,\, \sqrt{4} \cdot \sqrt{9} \cdot \sqrt{5} \)

\(\,\,\,\,\,\, 2 \cdot 3 \cdot \sqrt{5} \)

\(\,\,\,\,\,\, 6 \sqrt{5} \)

\(\textbf{6)}\) \( \sqrt{360} \)

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The answer is \( 6\sqrt{10} \)

\(\textbf{7)}\) \( \sqrt{75} \)

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The answer is \( 5\sqrt{3} \)

\(\textbf{8)}\) \( \sqrt{240} \)

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The answer is \( 4\sqrt{15} \)

\(\textbf{9)}\) \( \sqrt{98} \)

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The answer is \( 7\sqrt{2} \)

\(\textbf{10)}\) \( \sqrt{54} \)

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The answer is \( 3\sqrt{6} \)

Challenge Problems

\(\textbf{11)}\) \( 2\sqrt{12}+5\sqrt{27} \)

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The answer is \( 19\sqrt{3} \)

See Related Pages\(\)

\(\bullet\text{ Multiplying Square Roots}\)
\(\,\,\,\,\,\,\,\, \sqrt{5} \cdot \sqrt{125} …\)

\(\bullet\text{ Dividing Square Roots}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\sqrt{12}}{\sqrt{3}}…\)

\(\bullet\text{ Adding and Subtracting Square Roots}\)
\(\,\,\,\,\,\,\,\,3\sqrt{2}-7\sqrt{2}…\)

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