The multiplication of \(\sqrt{10}\) and \(\sqrt{5}\) can be simplified using the property of square roots that states \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\).
So, we have:
\[ \sqrt{10} \times \sqrt{5} = \sqrt{10 \times 5} = \sqrt{50} \]
Now, \(\sqrt{50}\) can be further simplified. Since \(50 = 25 \times 2\) and \(\sqrt{25} = 5\), we can write:
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]
Thus,
\[ \sqrt{10} \times \sqrt{5} = 5\sqrt{2} \]
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