Question

simplify root3+1/root3-1+root2+1/root2-1+root3-1/root3+1 + root 2-1/root2+1

Answer 1

Answer:

1+2+31+....+8+91

To find:

Value of \frac{1}{1+\sqrt 2}+\frac{1}{\sqrt{2}+\sqrt{3}}+....+\frac{1}{\sqrt{8}+\sqrt{9}}1+21+2+31+....+8+91

Solution:

By rationalization

\frac{1}{1+\sqrt 2}\times \frac{\sqrt{2}-1}{\sqrt{2}-1}+\frac{1}{\sqrt{2}+\sqrt{3}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}+....+\frac{1}{\sqrt{8}+\sqrt{9}}\times \frac{\sqrt{9}-\sqrt{8}}{\sqrt{9}-\sqrt{8}}1+21×2−12−1+2+31×3−23−2+....+8+91×9−89−8

\frac{\sqrt{2}-1}{(\sqrt{2})^2-1}+\frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2}+\frac{\sqrt{4}-\sqrt{3}}{(\sqrt{4})^2-(\sqrt{3})^2}+....\frac{\sqrt{9}-\sqrt{8}}{(\sqrt{9})^2-(\sqrt{8})^2}(2)2−12−1+(3)2−(2)23−2+(4)2−(3)24−3+....(9)2−(8)29−8

Using identity:

(a+b)(a-b)=a^2-b^2(a+b)(a−b)=

Step-by-step explanation:

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