Question

Give me the answer very fast please.​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\dfrac{1}{\sqrt{4}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{6}}+\dfrac{1}{\sqrt{6}+\sqrt{7}}+\dfrac{1}{\sqrt{7}+\sqrt{8}}+\dfrac{1}{\sqrt{8}+\sqrt{9}}}$

$\tt{=\dfrac{\sqrt{5}-\sqrt{4}}{\left(\sqrt{4}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{4}\right)}+\dfrac{\sqrt{6}-\sqrt{5}}{\left(\sqrt{5}+\sqrt{6}\right)\left(\sqrt{6}-\sqrt{5}\right)}+\dfrac{\sqrt{7}-\sqrt{6}}{\left(\sqrt{6}+\sqrt{7}\right)\left(\sqrt{7}-\sqrt{6}\right)}}\\\\\tt{+\dfrac{\sqrt{8}-\sqrt{7}}{\left(\sqrt{7}+\sqrt{8}\right)\left(\sqrt{8}-\sqrt{7}\right)}+\dfrac{\sqrt{9}-\sqrt{8}}{\left(\sqrt{8}+\sqrt{9}\right)\left(\sqrt{9}-\sqrt{8}\right)}}$

$\tt{=\dfrac{\sqrt{5}-\sqrt{4}}{5-4}+\dfrac{\sqrt{6}-\sqrt{5}}{6-5}+\dfrac{\sqrt{7}-\sqrt{6}}{7-6}+\dfrac{\sqrt{8}-\sqrt{7}}{8-7}+\dfrac{\sqrt{9}-\sqrt{8}}{9-8}}$

$\tt{=\sqrt{5}-\sqrt{4}+\sqrt{6}-\sqrt{5}+\sqrt{7}-\sqrt{6}+\sqrt{8}-\sqrt{7}+\sqrt{9}-\sqrt{8}}$

$\tt{=-\sqrt{4}+\sqrt{9}}$

$\tt{=-2+3}$

$\tt{=1}$