化简 sqrt(9-4\sqrt{5)}

解答

化简

9 - 45

5 - 2

十进制表示法

0.23606 \dots

求解步骤

9 - 45

= 5 - 45 + 4

= (5)^{2} - 45 + (4)^{2}

4 = 2

= (5)^{2} - 45 + 2^{2}

25 \cdot 2 = 45

= (5)^{2} - 25 \cdot 2 + 2^{2}

使用完全平方公式:

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

(5)^{2} - 25 \cdot 2 + 2^{2} = (5 - 2)^{2}

= (5 - 2)^{2}

使用根式运算法则:

(5 - 2)^{2} = 5 - 2

= 5 - 2

\frac{\frac{3}{4}}{4}

x^{2} - 20 = x

4 (2 x^{2} + 1) - 2 (4 x - 1) = 2 (2 x - 1)^{2}

x^{3} - 8 x^{2} + 15 x

\frac{3}{2} + (- \frac{6}{5})