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    Which of the following is correct?(i) √7 + √2 > √6 + √3(ii) √7 + √2 < √6 + √3(iii) √7 + √2 = √6 + √3
    Question

    Which of the following is correct?
    (i) √7 + √2 > √6 + √3
    (ii) √7 + √2 < √6 + √3
    (iii) √7 + √2 = √6 + √3

    A.

    (i)

    B.

    (ii)

    C.

    (iii)

    D.

    (i), (ii) and (iii)

    Correct option is B

    Given:
    √7 + √2 and √6 + √3
    Formula Used:
    If a > 0 and b > 0, then a > b ⇔ a² > b²
    Solution:
    (√7 + √2)² = 7 + 2 + 2√14 = 9 + 2√14
    (√6 + √3)² = 6 + 3 + 2√18 = 9 + 2√18
    Since √18 > √14,
    9 + 2√18 > 9 + 2√14
    Therefore, √6 + √3 > √7 + √2
    Hence, statement (ii) is correct.


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