簡約 (sqrt(2-\sqrt[3]{5)})^4

解

簡約

(2 - 35)^{4}

4 - 435 + 3 5^{2}

十進法表記

0.08411 \dots

解答ステップ

(2 - 35)^{4}

4

を書き換え

2 \cdot 2

= (2 - 35)^{2 \cdot 2}

指数の規則を適用する:

a^{b c} = (a^{b})^{c}, a \geq 0

(2 - 35)^{2 \cdot 2} = ((2 - 35)^{2})^{2}

= ((2 - 35)^{2})^{2}

指数の規則を適用する:

(n a)^{n} = a, n i s o dd or a \geq 0

(2 - 35)^{2} = 2 - 35

= (2 - 35)^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(2 - 35)^{2} = 2^{2} - 2 \cdot 235 + (35)^{2}

= 2^{2} - 2 \cdot 235 + (35)^{2}

2^{2} = 4

- 2 \cdot 235 = - 435

= 4 - 435 + (35)^{2}

(35)^{2} = 5^{\frac{2}{3}}

= 4 - 435 + 5^{\frac{2}{3}}

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

= 4 - 435 + 3 5^{2}