簡約 \sqrt[52]{1.025^4}

解

簡約

52 1.02 5^{4}

\frac{13 41}{13 40}

十進法表記

1.00190 \dots

解答ステップ

52 1.02 5^{4}

1.02 5^{4} = 1.10381 \dots

= 52 1.10381 \dots

1.10381 \dots = \frac{2825761}{2560000}

= 52 \frac{2825761}{2560000}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b}, a \geq 0, b \geq 0

= \frac{52 2825761}{52 2560000}

522825761 = 1341

= \frac{13 41}{52 2560000}

522560000 = 1340

= \frac{13 41}{13 40}