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Compare two sums or differences of surds by squaring

This type of question, asked 4 times: 12 Sep 2025 S2, 14 Sep 2025 S3, 18 Sep 2025 S2, 19 Sep 2025 S1. All 4 questions below, oldest first.

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  1. Question 1

    12 Sep 2025 S2

    51
    Let x=3+5x = \sqrt{3} + \sqrt{5} and y=8+2y = \sqrt{8} + \sqrt{2}. Which is greater?

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  2. Question 2

    14 Sep 2025 S3

    51
    If a = 7−3\sqrt{7} - \sqrt{3}, and b = 5−2\sqrt{5} - \sqrt{2}, then which of the following is true?

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  3. Question 3

    18 Sep 2025 S2

    53
    Identify the incorrect relationship(s) from the list below: (i) 6+2=5+3\sqrt{6} + \sqrt{2} = \sqrt{5} + \sqrt{3} (ii) 6+2<5+3\sqrt{6} + \sqrt{2} < \sqrt{5} + \sqrt{3} (iii) 6+2>5+3\sqrt{6} + \sqrt{2} > \sqrt{5} + \sqrt{3}

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  4. Question 4

    19 Sep 2025 S1

    53
    Which of the following is correct? (i) 7+2>6+3\sqrt{7} + \sqrt{2} > \sqrt{6} + \sqrt{3} (ii) 7+2<6+3\sqrt{7} + \sqrt{2} < \sqrt{6} + \sqrt{3} (iii) 7+2=6+3\sqrt{7} + \sqrt{2} = \sqrt{6} + \sqrt{3}

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