Giải Bài 2 trang 13 SGK Toán 11 Chân trời sáng tạo tập 2 - CTST

Lời giải chi tiết

a) \(3.\sqrt 3 .\sqrt[4]{3}.\sqrt[8]{3} \)\(= {3.3^{\frac{1}{2}}}{.3^{\frac{1}{4}}}{.3^{\frac{1}{8}}} \)\(= {3^{1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}}}\)\( = {3^{\frac{{15}}{8}}}\)

b) \(\sqrt {a\sqrt {a\sqrt a } } \)\(= \sqrt {a\sqrt {a.{a^{\frac{1}{2}}}} }\)\( = \sqrt {a\sqrt {{a^{1 + \frac{1}{2}}}} }\)\( = \sqrt {a\sqrt {{a^{\frac{3}{2}}}} } \)\(= \sqrt {a.{a^{\frac{3}{4}}}} \)\(= \sqrt {{a^{1 + \frac{3}{4}}}}\)\( = \sqrt {{a^{\frac{7}{4}}}} \)\(= {a^{\frac{7}{8}}}\)

c) \(\frac{{\sqrt a .\sqrt[3]{a}.\sqrt[4]{a}}}{{{{\left( {\sqrt[5]{a}} \right)}^3}.{a^{\frac{2}{5}}}}}\)\( = \frac{{{a^{\frac{1}{2}}}.{a^{\frac{1}{3}}}.{a^{\frac{1}{4}}}}}{{\sqrt[5]{{{a^3}}}.{a^{\frac{2}{5}}}}}\)\( = \frac{{{a^{\frac{1}{2} + \frac{1}{3} + \frac{1}{4}}}}}{{{a^{\frac{3}{5}}}.{a^{\frac{2}{5}}}}} \)\(= \frac{{{a^{\frac{{13}}{{12}}}}}}{{{a^{\frac{3}{5} + \frac{2}{5}}}}} \)\(= \frac{{{a^{\frac{{13}}{{12}}}}}}{a} \)\(= {a^{\frac{{13}}{{12}} - 1}} \)\(= {a^{\frac{1}{{12}}}}\)

-- Mod Toán 11 HỌC247