Question

Giải phương trình sau:

\(\sqrt{313^2-312^2}.\left(\sqrt{\dfrac{49}{8}}:\sqrt{3\dfrac{1}{8}}\right)\)

Answer 1

\(\sqrt{313^2-312^2}\cdot\left(\sqrt{\dfrac{49}{8}}:\sqrt{3\dfrac{1}{8}}\right)\)

\(=\sqrt{\left(313-312\right)\left(313+312\right)}\cdot\left(\sqrt{\dfrac{49}{8}}:\sqrt{\dfrac{25}{8}}\right)\)

\(=\sqrt{1\cdot625}\cdot\left(\sqrt{\dfrac{49}{8}:\dfrac{25}{8}}\right)\)

\(=\sqrt{625}\cdot\left(\sqrt{\dfrac{49}{8}\cdot\dfrac{8}{25}}\right)\)

\(=25\cdot\left(49\cdot\dfrac{1}{25}\right)\)

\(=25\cdot\left(7\cdot\dfrac{1}{5}\right)\)

\(=25\cdot\dfrac{7}{5}\)

\(=35\)