簡約 sqrt(\sqrt[3]{81)}

解

簡約

381

3 3^{2}

十進法表記

2.08008 \dots

解答ステップ

381

381 = 333

= 333

累乗根の規則を適用する:

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

333 = 333

= 333

33 = 63

= 363

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}} 63

累乗根の規則を適用する:

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

63 = 3^{\frac{1}{6}}

= 3^{\frac{1}{2}} \cdot 3^{\frac{1}{6}}

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

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

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

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

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

= 3 3^{2}