a) \(\sqrt{45}=\sqrt{9.5}=3\sqrt{5}\)
\(\sqrt{32+16\sqrt{3}}=\sqrt{16\left(2+\sqrt{3}\right)}=4\sqrt{2+\sqrt{3}}\)
\(\sqrt{8x^2}=\sqrt{4x^2.2}=2x\sqrt{2}\left(x\ge0\right)\)
\(\sqrt{75y}=\sqrt{25.3y}=5\sqrt{3y}\left(y\ge0\right)\)
b) \(10\sqrt{3}=\sqrt{100.3}=\sqrt{300}\)
\(-8\sqrt{5}=-\sqrt{64.5}=-\sqrt{320}\)
\(5\sqrt{\dfrac{33}{15}}=\sqrt{25.\dfrac{33}{15}}=\sqrt{15}\)
\(-x\sqrt{\dfrac{125}{x}}=-\sqrt{x^2.\dfrac{125}{x}}=-\sqrt{125x}\)
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