It sounds like you might be looking for a quick check or practice problems on the topic of products of irrational square roots. Here are some example problems and their solutions to help you test your understanding:
Quick Check Problems
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Simplify the expression: \(\sqrt{2} \times \sqrt{3}\)
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Simplify the expression: \(\sqrt{5} \times \sqrt{8}\)
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Simplify the expression: \(\sqrt{7} \times \sqrt{14}\)
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Simplify the expression: \(\sqrt{12} \times \sqrt{3}\)
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Simplify the expression: \(2\sqrt{3} \times 3\sqrt{2}\)
Solutions
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\(\sqrt{2} \times \sqrt{3} = \sqrt{2 \times 3} = \sqrt{6}\)
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\(\sqrt{5} \times \sqrt{8} = \sqrt{5 \times 8} = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}\)
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\(\sqrt{7} \times \sqrt{14} = \sqrt{7 \times 14} = \sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\)
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\(\sqrt{12} \times \sqrt{3} = \sqrt{12 \times 3} = \sqrt{36} = 6\)
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\(2\sqrt{3} \times 3\sqrt{2} = (2 \times 3) (\sqrt{3} \times \sqrt{2}) = 6\sqrt{6}\)
Summary
When dealing with the product of square roots, remember that \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\). If the product results in a square root with a perfect square, simplifying further can often yield neat integers or simple expressions.
Feel free to ask if you need more problems or further explanations on any of the concepts!
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