Question

Rút gọn biểu thức \(\sqrt {x\sqrt {x\sqrt x } } :{x^{\frac{5}{8}}}(x > 0)\) ta được

A. \(\sqrt[4]{x}\)                         

B. \(\sqrt x \).                   

C. \(\sqrt[3]{x}\).                        

D. \(\sqrt[5]{x}\)

 

Answer 1

\(=\sqrt{x\sqrt{x^{1+\dfrac{1}{2}}}}:x^{\dfrac{5}{8}}\)

\(=\sqrt{x\cdot x^{\dfrac{1}{2}\cdot\dfrac{3}{2}}}:x^{\dfrac{5}{8}}\)

\(=\sqrt{x^{1+\dfrac{3}{4}}}:x^{\dfrac{5}{8}}\)

\(=x^{\dfrac{1}{2}\cdot\dfrac{7}{4}}:x^{\dfrac{5}{8}}=x^{\dfrac{7}{8}-\dfrac{5}{8}}=x^{\dfrac{1}{4}}=\sqrt[4]{x}\)

=>A