10th Class Mathematics Real Numbers Question Bank Real Number

  • question_answer
    The value of \[\frac{\mathbf{1}}{\mathbf{1+}\sqrt{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{2}}\mathbf{+}\sqrt{\mathbf{3}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}\mathbf{+}\sqrt{\mathbf{4}}}\mathbf{+}.......\]\[\frac{\mathbf{1}}{\sqrt{\mathbf{34}}\mathbf{+}\sqrt{\mathbf{35}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{35}}\mathbf{+}\sqrt{\mathbf{36}}}\] is

    A)  0                                

    B)  2           

    C)  3                                

    D)  5

    Correct Answer: D

    Solution :

    (d): Follow the same procedure as in previous question. (Multiplying successive term by\[\left( \sqrt{2}-1 \right),\left( \sqrt{3}-\sqrt{2} \right),....,\left( \sqrt{36}-\sqrt{35} \right)\] lead to rationalization of each terms. Middle terms cancel. What remain is\[\sqrt{36}-1=6-1=5)\]


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