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Square root of a +- 2 sqrt b written as (sqrt x +- sqrt y)

This type of question, asked 6 times: CDS 2 2016, CDS 1 2019, CDS 1 2021, CDS 2 2021, CDS 1 2023, CDS 1 2025. All 6 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    3
    What is 62+72+82+92+1027+43−4+23\frac{6^2 + 7^2 + 8^2 + 9^2 + 10^2}{\sqrt{7 + 4\sqrt{3}} - \sqrt{4 + 2\sqrt{3}}} equal to ?

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  2. Question 2

    CDS 1 2019

    76
    What is the square root of 16+6716 + 6\sqrt{7} ?

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  3. Question 3

    CDS 1 2021

    42
    What is the square root of 15−41415 - 4\sqrt{14}?

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  4. Question 4

    CDS 2 2021

    3
    What is the square root of 23−41523-4\sqrt{15} ?

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  5. Question 5

    CDS 1 2023

    14
    If the positive square root of (5+32)(5−32)(5 + 3\sqrt{2})(5 - 3\sqrt{2}) is α\alpha, then what is the positive square root of 8+2α8 + 2\alpha?

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  6. Question 6

    CDS 1 2025

    41
    What is 17−415+8−215\sqrt{17 - 4\sqrt{15}} + \sqrt{8 - 2\sqrt{15}} equal to ?

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