Question

Answer 1

a) \(A=\left(\sqrt{12}+\sqrt{75}+\sqrt{27}\right):\sqrt{15}\)

\(\Leftrightarrow A=\left(2\sqrt{3}+5\sqrt{3}+3\sqrt{3}\right):\sqrt{3}.\sqrt{5}\)

\(\Leftrightarrow A=10\sqrt{3}:\left(\sqrt{3}.\sqrt{5}\right)=\dfrac{10}{\sqrt{5}}=5\sqrt{5}\)

b) \(B=\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)

\(\Leftrightarrow B=\left(60\sqrt{2}-80\sqrt{2}+105\sqrt{2}\right):\sqrt{10}\)

\(\Leftrightarrow85\sqrt{2}:\left(\sqrt{2}.\sqrt{5}\right)=\dfrac{85}{\sqrt{5}}=17\sqrt{5}\)