簡約 sqrt(4+\sqrt{12)}

解

簡約

4 + 12

3 + 1

十進法表記

2.73205 \dots

解答ステップ

4 + 12

12 = 23

= 4 + 23

= 3 + 23 + 1

= (3)^{2} + 23 + (1)^{2}

1 = 1

= (3)^{2} + 23 + 1^{2}

23 \cdot 1 = 23

= (3)^{2} + 23 \cdot 1 + 1^{2}

完全平方式を適用する:

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

(3)^{2} + 23 \cdot 1 + 1^{2} = (3 + 1)^{2}

= (3 + 1)^{2}

累乗根の規則を適用する:

n a^{n} = a

(3 + 1)^{2} = 3 + 1

= 3 + 1