簡約 (5/2-1)(5/2-1)sqrt(pi)

解

簡約

(\frac{5}{2} - 1) (\frac{5}{2} - 1) π

\frac{9 π}{4}

十進法表記

3.98802 \dots

解答ステップ

(\frac{5}{2} - 1) (\frac{5}{2} - 1) π

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

(\frac{5}{2} - 1) (\frac{5}{2} - 1) = (\frac{5}{2} - 1)^{1 + 1}

= (\frac{5}{2} - 1)^{1 + 1} π

数を足す:

1 + 1 = 2

= (\frac{5}{2} - 1)^{2} π

(\frac{5}{2} - 1)^{2} = \frac{3 ^{2}}{2 ^{2}}

= π \frac{3 ^{2}}{2 ^{2}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ^{2} π}{2 ^{2}}

3^{2} = 9

= \frac{9 π}{2 ^{2}}

2^{2} = 4

= \frac{9 π}{4}