簡約 sqrt(25x^2-100x*y^2+100y^4)

解

簡約

25 x^{2} - 100 x \cdot y^{2} + 100 y^{4}

5 (x - 2 y^{2})

解答ステップ

25 x^{2} - 100 x y^{2} + 100 y^{4}

因数

25 x^{2} - 100 x y^{2} + 100 y^{4} : 25 (x^{2} - 4 x y^{2} + 4 y^{4})

= 25 (x^{2} - 4 x y^{2} + 4 y^{4})

累乗根の規則を適用する:

n ab = n a n b,

, 以下を想定

a \geq 0, b \geq 0

= 25 x^{2} - 4 x y^{2} + 4 y^{4}

25 = 5

= 5 x^{2} - 4 x y^{2} + 4 y^{4}

因数

x^{2} - 4 x y^{2} + 4 y^{4} : (x - 2 y^{2})^{2}

= 5 (x - 2 y^{2})^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

(x - 2 y^{2})^{2} = x - 2 y^{2}

= 5 (x - 2 y^{2})