簡約 sqrt((3-\sqrt{10))^2}

解

簡約

(3 - 10)^{2}

10 - 3

十進法表記

0.16227 \dots

解答ステップ

(3 - 10)^{2}

(3 - 10)^{2} = 19 - 610

= 19 - 610

= 10 - 610 + 9

= (10)^{2} - 610 + (9)^{2}

9 = 3

= (10)^{2} - 610 + 3^{2}

210 \cdot 3 = 610

= (10)^{2} - 210 \cdot 3 + 3^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(10)^{2} - 210 \cdot 3 + 3^{2} = (10 - 3)^{2}

= (10 - 3)^{2}

累乗根の規則を適用する:

n a^{n} = a

(10 - 3)^{2} = 10 - 3

= 10 - 3