Simplify the following mathematical expressions: 1. \(\sqrt{13 \cdot 18 \cdot \sqrt{26}}\) 2. \((\sqrt{45} - \sqrt{5}) \cdot \sqrt{5}\) 3. \(\sqrt{\frac{1}{25}} \cdot x^8y^2 \text{ при } x = 3 \text{ и } y = 5\) 4. \(\sqrt{a^8} \cdot (-a)^4 \text{ при } a = 2\)

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Accepted Answer

\(
\(\sqrt{13 \cdot 18 \cdot \sqrt{26}}\)
\)
\(
\((\sqrt{45} - \sqrt{5}) \cdot \sqrt{5}\) = \(\sqrt{45}\) \(\cdot\) \(\sqrt{5}\) - \(\sqrt{5}\) \(\cdot\) \(\sqrt{5}\) = \(\sqrt{45 \cdot 5}\) - 5 = \(\sqrt{225}\) - 5 = 15 - 5 = 10
\)
\(
\(\sqrt{\frac{1}{25}} \cdot x^8y^2 = \frac{1}{5} x^8y^2\)
\)
При \(x = 3\) и \(y = 5\):
\(\frac{1}{5} \cdot (3)^8 \cdot (5)^2 = \frac{1}{5} \cdot 6561 \cdot 25 = 6561 \cdot 5 = 32805
\)
\(
\(\sqrt{a^8} = a^4\)
\)
\(a^4 \cdot (-a)^4 = a^4 \cdot a^4 = a^8\)
При \(a = 2\):
\(2^8 = 256
\)

Ответ: 1. \(\sqrt{13 \cdot 18 \cdot \sqrt{26}}\), 2. 10, 3. 32805, 4. 256.