Question

5/√7+√2 - √8-2√7 +√2

Answer 1

\(\dfrac{5}{\sqrt{7}+\sqrt{2}}-\sqrt{8-2\sqrt{7}}+\sqrt{2}\)

\(=\dfrac{\sqrt{7}-\sqrt{2}}{5}\cdot5-\sqrt{\left(\sqrt{7}-1\right)^2}+\sqrt{2}\)

\(=\sqrt{7}-\sqrt{2}+\sqrt{2}-\left|\sqrt{7}-1\right|\)

\(=\sqrt{7}-\sqrt{7}+1=1\)

Answer 2

\(\dfrac{5}{\sqrt{7}+\sqrt{2}}-\sqrt{8-2\sqrt{7}}+\sqrt{2}\\ =\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{7-2}-\sqrt{7-2\sqrt{7}+1}+\sqrt{2}\\ =\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{5}-\sqrt{\left(\sqrt{7}\right)^2-2\cdot\sqrt{7}\cdot1+1^2}+\sqrt{2}\\ =\sqrt{7}-\sqrt{2}-\sqrt{\left(\sqrt{7}-1\right)^2}+\sqrt{2}\\ =\sqrt{7}-\sqrt{2}-\sqrt{7}+1+\sqrt{2}\\ =1\)