簡約 sqrt(3x^2)\sqrt[3]{6x^3}\sqrt[4]{4x^2}

解

簡約

3 x^{2} 3 6 x^{3} 4 4 x^{2}

6 6^{5} x^{2} 4 x^{2}

解答ステップ

3 x^{2} 3 6 x^{3} 4 4 x^{2}

簡素化

3 x^{2} : 3 x

= 3 x 3 6 x^{3} 4 4 x^{2}

簡素化

3 6 x^{3} : 36 x

= 3 x 36 x 4 4 x^{2}

簡素化

4 4 x^{2} : 2 4 x^{2}

= 3 x 36 x 2 4 x^{2}

32 = 6

= 6 x 36 x 4 x^{2}

累乗根の規則を適用する:

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

6 = 6^{\frac{1}{2}}

= 6^{\frac{1}{2}} x 36 x 4 x^{2}

累乗根の規則を適用する:

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

36 = 6^{\frac{1}{3}}

= 6^{\frac{1}{2}} x \cdot 6^{\frac{1}{3}} x 4 x^{2}

6^{\frac{1}{2}} \cdot 6^{\frac{1}{3}} = 6^{\frac{5}{6}}

= 6^{\frac{5}{6}} xx 4 x^{2}

指数の規則を適用する:

aa = a^{2}

xx = x^{2}

= 6^{\frac{5}{6}} x^{2} 4 x^{2}

6^{\frac{5}{6}} = 6 6^{5}

= 6 6^{5} x^{2} 4 x^{2}