簡約 \sqrt[3]{1.9059}^2

解

簡約

3 1.9059^{2}

\frac{3 1905 9 ^{2}}{100 3 1 0 ^{2}}

十進法表記

1.53721 \dots

解答ステップ

(3 1.9059)^{2}

3 1.9059 = \frac{3 19059}{10 3 10}

= (\frac{3 19059}{10 3 10})^{2}

指数の規則を適用する:

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

= \frac{( 3 19059 ) ^{2}}{( 10 3 10 ) ^{2}}

(10310)^{2} = 100 \cdot 1 0^{\frac{2}{3}}

= \frac{( 3 19059 ) ^{2}}{100 \cdot 1 0 ^{\frac{2}{3}}}

(319059)^{2} = 1905 9^{\frac{2}{3}}

= \frac{1905 9 ^{\frac{2}{3}}}{100 \cdot 1 0 ^{\frac{2}{3}}}

1905 9^{\frac{2}{3}} = 3 1905 9^{2}

= \frac{3 1905 9 ^{2}}{100 3 1 0 ^{2}}

1 0^{\frac{2}{3}} = 3 1 0^{2}

= \frac{3 1905 9 ^{2}}{100 3 1 0 ^{2}}