Question

Simplify this question

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

1

Step-by-step explanation:

$\dfrac{1}{\sqrt{4} + \sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{6}}+\dfrac{1}{\sqrt{6}+\sqrt{7}}+\dfrac{1}{\sqrt{7}+\sqrt{8}}+\dfrac{1}{\sqrt{8}+\sqrt{9}}\\\\\\\\= \dfrac{1}{2 + \sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{6}}+\dfrac{1}{\sqrt{6}+\sqrt{7}}+\dfrac{1}{\sqrt{7}+2\sqrt{2}}+\dfrac{1}{2\sqrt{2}+3}$

$= \dfrac{2 - \sqrt{5}}{(2)^2 - (\sqrt{5})^2}+\dfrac{\sqrt{5} - \sqrt{6}}{(\sqrt{5})^2-(\sqrt{6})^2}+\dfrac{\sqrt{6}-\sqrt{7}}{(\sqrt{6})^2-(\sqrt{7})^2}+\dfrac{\sqrt{7}-2\sqrt{2}}{(\sqrt{7})^2-(2\sqrt{2})^2}+\dfrac{2\sqrt{2} - 3}{(2\sqrt{2})^2-(3)^2}\\\\\\\\\\= \dfrac{2 - \sqrt{5}}{4 - 5} + \dfrac{\sqrt{5}-\sqrt{6}}{5-6} + \dfrac{\sqrt{6}-\sqrt{7}}{6-7} + \dfrac{\sqrt{7}-2\sqrt{2}}{7 - 8} + \dfrac{2\sqrt{2}-3}{8-9}$

$= \dfrac{2 - \sqrt{5}}{-1} + \dfrac{\sqrt{5}-\sqrt{6}}{-1} + \dfrac{\sqrt{6}-\sqrt{7}}{-1} + \dfrac{\sqrt{7}-2\sqrt{2}}{-1} + \dfrac{2\sqrt{2}-3}{-1}\\\\\\\\\\= -2 + \sqrt{5} - \sqrt{5} + \sqrt{6} - \sqrt{6} + \sqrt{7} - \sqrt{7} + 2\sqrt{2} - 2\sqrt{2} + 3\\\\\\= 3 - 2\\\\\\= \boxed{\boxed{\boxed{\bold{1}}}}$