簡約 400^{1/4}

解

簡約

40 0^{\frac{1}{4}}

2 \cdot 5^{\frac{1}{2}}

十進法表記

4.47213 \dots

解答ステップ

40 0^{\frac{1}{4}}

数を因数に分解する:

400 = 2 0^{2}

= (2 0^{2})^{\frac{1}{4}}

指数の規則を適用する:

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

= 2 0^{2 \cdot \frac{1}{4}}

2 \cdot \frac{1}{4} = \frac{1}{2}

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

以下の素因数分解:

20 : 2^{2} \cdot 5

= (2^{2} \cdot 5)^{\frac{1}{2}}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(2^{2} \cdot 5)^{\frac{1}{2}} = (2^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

= (2^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

(2^{2})^{\frac{1}{2}} = 2

= 2 \cdot 5^{\frac{1}{2}}