Giải:
a) \(\left(\sqrt{3}+2\sqrt{5}\right)\sqrt{3}-\sqrt{60}\)
\(=\sqrt{3}.\sqrt{3}+2\sqrt{5}.\sqrt{3}-\sqrt{60}\)
\(=3+2\sqrt{15}-\sqrt{60}\)
\(=3+2\sqrt{15}-2\sqrt{15}\)
\(=3\)
Vậy ...
b) \(\left(15\sqrt{200}-3\sqrt{450}+2\sqrt{50}\right):\sqrt{10}\)
\(=\left(15\sqrt{4.50}-3\sqrt{9.50}+2\sqrt{50}\right):\sqrt{10}\)
\(=\left(30\sqrt{50}-9\sqrt{50}+2\sqrt{50}\right):\sqrt{10}\)
\(=23\sqrt{50}:\sqrt{10}\)
\(=\dfrac{23\sqrt{50}}{\sqrt{10}}\)
\(=\dfrac{23\sqrt{5}\sqrt{10}}{\sqrt{10}}\)
\(=23\sqrt{5}\)
Vậy ...
\(a\text{) }\left(\sqrt{3}+2\sqrt{5}\right)\sqrt{3}-\sqrt{60}\\ =3+2\sqrt{15}-2\sqrt{15}=3\)
\(b\text{) }\left(15\sqrt{200}-3\sqrt{450}+2\sqrt{50}\right):\sqrt{10}\\ =15\sqrt{20}-3\sqrt{45}+2\sqrt{5}\\ =30\sqrt{5}-9\sqrt{5}+2\sqrt{5}\\ =\left(30-9+2\right)\sqrt{5}=23\sqrt{5}\)
