Question

( sqrt 5 +2)(1- sqrt 2 0)+45/ sqrt 5 + sqrt 20​

Answer 1

$\dfrac{( \sqrt 5 +2)(1- \sqrt {2 0})+45}{ \sqrt {5 }+ \sqrt{ 20}}$

$\begin{aligned} &(\sqrt{5}+2)(1-\sqrt{20})+\frac{45}{\sqrt{5}+\sqrt{20}} \\ \\ =&(\sqrt{5}+2)(1-\sqrt{20})+\frac{45}{\sqrt{5}+\sqrt{5 \times 4}} \\ \\ =&(\sqrt{5}+2)(1-\sqrt{20})+\frac{45}{\sqrt{5}+2 \sqrt{5}} \\ \\ =&(\sqrt{5}+2)(1-\sqrt{20})+\frac{45}{3 \sqrt{5}} \\ \\ =& \sqrt{5}(1-\sqrt{20})+2(1-\sqrt{20})+\frac{15}{\sqrt{5}} \\ \\ =& \sqrt{5}-\sqrt{20 \times 5}+2-2 \sqrt{20}+\frac{15 \sqrt{5}}{5} \\ \\ =& \sqrt{5}-\sqrt{100}+2-2 \sqrt{20}+3 \sqrt{5} \\ \\ =& \sqrt{5}+3 \sqrt{5}-10+2-2 \sqrt{20} \\ \\ =& 4 \sqrt{5}-2 \cdot \sqrt{4 \times 5}-8 \\ \\ =& 4 \sqrt{5}-2 \times 2 \sqrt{5}-8 \\ \\ =& 4 \sqrt{5}-4 \sqrt{5}-8 \\ \\ \color{red} =& \color{red}-8 \end{aligned}$