簡約 sqrt((\sqrt{27)-(2sqrt(12)+sqrt(6)))^2}

解

簡約

(27 - (212 + 6))^{2}

6 + 3

十進法表記

4.18154 \dots

解答ステップ

(27 - (212 + 6))^{2}

(27 - (212 + 6))^{2} = 9 + 62

= 9 + 62

= 6 + 62 + 3

= 3 \cdot 2 + 62 + 3

= (3)^{2} (2)^{2} + 62 + (3)^{2}

2323 = 62

= (32)^{2} + 2323 + (3)^{2}

完全平方式を適用する:

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

(32)^{2} + 2323 + (3)^{2} = (32 + 3)^{2}

= (32 + 3)^{2}

累乗根の規則を適用する:

n a^{n} = a

(32 + 3)^{2} = 32 + 3

= 32 + 3

32 = 6

= 6 + 3