Question

Thực hiện phép tính:

a) \(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right):\sqrt{3}\)

b) \(\left(\sqrt{125}+\sqrt{245}-\sqrt{5}\right):\sqrt{5}\)

c) \(\left(\sqrt{\dfrac{1}{7}}-\sqrt{\dfrac{16}{7}}+\sqrt{7}\right):\sqrt{7}\)

Answer 1

a) \(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right):\sqrt{3}=7\sqrt{16}+3\sqrt{9}-2\sqrt{4}\)

\(=7.4+3.3-2.2=28+9-4=33\)

b) \(\left(\sqrt{125}+\sqrt{245}-\sqrt{5}\right):\sqrt{5}=\sqrt{25}+\sqrt{49}-1\)

\(=5+7-1=11\)

c) \(\left(\sqrt{\dfrac{1}{7}}-\sqrt{\dfrac{16}{7}}+\sqrt{7}\right):\sqrt{7}=\left(\dfrac{\sqrt{1}}{\sqrt{7}}-\dfrac{\sqrt{16}}{\sqrt{7}}+\sqrt{7}\right):\sqrt{7}\)

\(=\left(\dfrac{1}{\sqrt{7}}-\dfrac{4}{\sqrt{7}}+\sqrt{7}\right):\sqrt{7}=\dfrac{1}{\sqrt{7}.\sqrt{7}}-\dfrac{4}{\sqrt{7}.\sqrt{7}}+1\)

\(=\dfrac{1}{7}-\dfrac{4}{7}+1=\dfrac{1}{7}-\dfrac{4}{7}+\dfrac{7}{7}\Leftrightarrow\dfrac{1-4+7}{7}=\dfrac{4}{7}\)