8th Class Mathematics Squares and Square Roots Question Bank Square and Square Roots

  • question_answer Find the value of the given expression\[2+\frac{1}{\sqrt{2}}+\frac{1}{2+\sqrt{2}}+\frac{1}{\sqrt{2}-2}\]?

    A)  \[2+\frac{1}{\sqrt{2}}\]           

    B)  \[-\frac{1}{\sqrt{2}}\]

    C)  \[2-\frac{1}{\sqrt{2}}\] 

    D)  \[\frac{1}{\sqrt{2}}\]

    Correct Answer: C

    Solution :

    (c): Rationalizing, we get \[2+\frac{\sqrt{2}}{2}+\frac{2-\sqrt{2}}{2}+\frac{2+\sqrt{2}}{-2}\] \[=2+\frac{\cancel{\sqrt{2}}+\cancel{\sqrt{2}}-\cancel{\sqrt{2}}-2-\sqrt{2}}{2}\] \[=2-\frac{\sqrt{2}}{2}=2-\frac{1}{\sqrt{2}}\].

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