簡約 (\sqrt[3]{91.6732400000000…})^2

解

簡約

(3 91.6732400000000 \dots)^{2}

\frac{3 229183 1 ^{2}}{100 3 2 5 ^{2}}

十進法表記

20.33113 \dots

解答ステップ

(3 91.67324)^{2}

3 91.67324 = \frac{3 2291831}{10 3 25}

= (\frac{3 2291831}{10 3 25})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 2291831 ) ^{2}}{( 10 3 25 ) ^{2}}

(10325)^{2} = 100 \cdot 2 5^{\frac{2}{3}}

= \frac{( 3 2291831 ) ^{2}}{100 \cdot 2 5 ^{\frac{2}{3}}}

(32291831)^{2} = 229183 1^{\frac{2}{3}}

= \frac{229183 1 ^{\frac{2}{3}}}{100 \cdot 2 5 ^{\frac{2}{3}}}

229183 1^{\frac{2}{3}} = 3 229183 1^{2}

= \frac{3 229183 1 ^{2}}{100 3 2 5 ^{2}}

2 5^{\frac{2}{3}} = 3 2 5^{2}

= \frac{3 229183 1 ^{2}}{100 3 2 5 ^{2}}