簡約 (sqrt(32)-sqrt(5))^{1/3}(sqrt(32)+sqrt(5))^{1/3}

解

簡約

(32 - 5)^{\frac{1}{3}} (32 + 5)^{\frac{1}{3}}

3

解答ステップ

(32 - 5)^{\frac{1}{3}} (32 + 5)^{\frac{1}{3}}

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m}

(32 - 5)^{\frac{1}{3}} (32 + 5)^{\frac{1}{3}} = ((32 - 5) (32 + 5))^{\frac{1}{3}}

= ((32 - 5) (32 + 5))^{\frac{1}{3}}

(32 - 5) (32 + 5) = 27

= 2 7^{\frac{1}{3}}

数を因数に分解する:

27 = 3^{3}

= (3^{3})^{\frac{1}{3}}

指数の規則を適用する:

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

(3^{3})^{\frac{1}{3}} = 3^{3 \cdot \frac{1}{3}} = 3

= 3