Question

Thực hiện tính \(\sqrt{48}+\sqrt{\dfrac{16}{3}}+10\sqrt{3}-5\sqrt{\dfrac{4}{3}}\)

Answer 1

\(\sqrt{48}+\sqrt{\dfrac{16}{3}}+10\sqrt{3}-5\sqrt{\dfrac{4}{3}}\)

\(=\sqrt{4^2.3}+\sqrt{4^2.\dfrac{1}{3}}+10\sqrt{3}-5\sqrt{2^2.\dfrac{1}{3}}\)

\(=4\sqrt{3}+4\sqrt{\dfrac{1}{3}}+10\sqrt{3}-5.2\sqrt{\dfrac{1}{3}}\)

\(=14\sqrt{3}-6\sqrt{\dfrac{1}{3}}\)

\(=14\sqrt{3}-6\sqrt{\dfrac{1}{9}.3}\)

\(=14\sqrt{3}-6.\dfrac{1}{3}\sqrt{3}=12\sqrt{3}\)

 

Answer 2

\(=4\sqrt{3}+\dfrac{4\sqrt{3}}{3}+10\sqrt{3}-5\cdot\dfrac{2\sqrt{3}}{3}\)

\(=14\sqrt{3}-\dfrac{6\sqrt{3}}{3}=12\sqrt{3}\)