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Products and quotients of square roots of decimals: simplify under one root

This type of question, asked 3 times: 15 Nov 2020 Tier II, 8 Aug 2022 Tier II, 26 Oct 2023 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    37
    Let x=(18753888÷1200768)×1751792x = \left(\frac{\sqrt{1875}}{\sqrt{3888}} \div \frac{\sqrt{1200}}{\sqrt{768}}\right) \times \frac{\sqrt{175}}{\sqrt{1792}}. Then x\sqrt{x} is equal to:

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  2. Question 2

    8 Aug 2022 Tier II

    41
    What is the value of 29.161.1664+0.2916116.64+0.00360.36\frac{\sqrt{29.16}}{\sqrt{1.1664}} + \frac{\sqrt{0.2916}}{\sqrt{116.64}} + \frac{\sqrt{0.0036}}{\sqrt{0.36}}?

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  3. Question 3

    26 Oct 2023 Tier II

    27
    Find the value of 1.24×2.792.64×5.94\frac{\sqrt{1.24} \times \sqrt{2.79}}{\sqrt{2.64} \times \sqrt{5.94}}

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