簡約 sqrt(12*4\sqrt{3)}

解

簡約

12 \cdot 43

4 4 3^{3}

十進法表記

9.11802 \dots

解答ステップ

12 \cdot 43

数を乗じる:

12 \cdot 4 = 48

= 483

累乗根の規則を適用する:

ab = a b, a \geq 0, b \geq 0

483 = 483

= 483

3 = 43

= 4843

48 = 43

= 4343

累乗根の規則を適用する:

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

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

= 4 \cdot 3^{\frac{1}{2}} 43

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

43 = 3^{\frac{1}{4}}

= 4 \cdot 3^{\frac{1}{2}} \cdot 3^{\frac{1}{4}}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

3^{\frac{1}{2}} \cdot 3^{\frac{1}{4}} = 3^{\frac{1}{2} + \frac{1}{4}}

= 4 \cdot 3^{\frac{1}{2} + \frac{1}{4}}

\frac{1}{2} + \frac{1}{4} = \frac{3}{4}

= 4 \cdot 3^{\frac{3}{4}}

= 3^{\frac{3}{4}} \cdot 4

3^{\frac{3}{4}} = 4 3^{3}

= 4 3^{3} \cdot 4

= 4 4 3^{3}