簡約 sqrt(\sqrt[3]{243)}

解

簡約

3243

6 3^{5}

十進法表記

2.49804 \dots

解答ステップ

3243

3243 = 339

= 339

累乗根の規則を適用する:

ab = a b, a \geq 0, b \geq 0

339 = 339

= 339

39 = 33

= 333

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

3 = 3^{\frac{1}{2}}

= 3^{\frac{1}{2}} 33

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

33 = 3^{\frac{1}{3}}

= 3^{\frac{1}{2}} \cdot 3^{\frac{1}{3}}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

3^{\frac{1}{2}} \cdot 3^{\frac{1}{3}} = 3^{\frac{1}{2} + \frac{1}{3}}

= 3^{\frac{1}{2} + \frac{1}{3}}

\frac{1}{2} + \frac{1}{3} = \frac{5}{6}

= 3^{\frac{5}{6}}

3^{\frac{5}{6}} = 6 3^{5}

= 6 3^{5}