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a) Ta có: \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}\)
\(=\left(-\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}\)
\(=-2+2\sqrt{5}-\sqrt{5}\)
\(=-2+\sqrt{5}\)
b) \(\left(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\sqrt{200}\right)\div\frac{1}{8}\)
\(=\left(\frac{\sqrt{2}}{4}-\frac{3\sqrt{2}}{2}+8\sqrt{2}\right)\cdot8\)
\(=\frac{27\sqrt{2}}{4}\cdot8\)
\(=54\sqrt{2}\)
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a, \(5\sqrt{\left(-2\right)^4}=5\sqrt{2^4}=5.2^2=5.4=20\)
b, \(-4\sqrt{\left(-3\right)^6}=-4\sqrt{3^6}=-4.3^3=-4.27=-108\)
c,\(\sqrt{\sqrt{\left(-5\right)^8}}=\sqrt{\sqrt{5^8}}=\sqrt{5^4}=5^2=25\)
d ,\(2\sqrt{\left(-5\right)^6}+3\sqrt{\left(-2\right)^8}\)
\(=2\sqrt{5^6}+3\sqrt{2^8}\)
=\(2.5^3+3.2^4=2.125+3.16=298\)
a) \(5\sqrt{\left(-2\right)^4}\) \(=5\left|\left(-2\right)^2\right|=5.4=20\)
b) \(-4\sqrt{\left(-3\right)^6}=-4\left|\left(-3\right)^3\right|=-4.27=-108\)
c) \(\sqrt{\sqrt{\left(-5\right)^8}}=\left|\left(-5\right)^4\right|=5^4=625\)
d) \(2\sqrt{\left(-5\right)^6}+3\sqrt{\left(-2\right)^8}\) \(=2\left|\left(-5\right)^3\right|+3\left|\left(-2\right)^4\right|\)
\(=-2.\left(-125\right)+3.16\)
\(= 250 + 48 = 298\)