簡約 sqrt(39+12\sqrt{3)}

解

簡約

39 + 123

3 + 6

十進法表記

7.73205 \dots

解答ステップ

39 + 123

= 3 + 123 + 36

= (3)^{2} + 123 + (36)^{2}

36 = 6

= (3)^{2} + 123 + 6^{2}

23 \cdot 6 = 123

= (3)^{2} + 23 \cdot 6 + 6^{2}

完全平方式を適用する:

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

(3)^{2} + 23 \cdot 6 + 6^{2} = (3 + 6)^{2}

= (3 + 6)^{2}

累乗根の規則を適用する:

n a^{n} = a

(3 + 6)^{2} = 3 + 6

= 3 + 6