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Square root of a quartic polynomial that is a perfect square

This type of question, asked 2 times: CDS 1 2020, CDS 2 2020. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2020

    23
    If the area of a square is 2401x4+196x2+42401x^4 + 196x^2 + 4, then what is its side length ?

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  2. Question 2

    CDS 2 2020

    35
    What is the square root of 4x4+8x3−4x+14x^4 + 8x^3 - 4x + 1 ?

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