How to simplify square root

Square root simplification
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[sy]

Thank you for explaining. The calculation in this video is a little complicated. If I were the instructor, I would calculated as follows:
√32 + √24 = √8 (√4 + √3), √32 - √24 = √8 (√4 - √3) ∴ (√32 + √24) / (√32 - √24) = (√4 + √3) / (√4 - √3)
(√4 + √3)(√4 + √3) / (√4 - √3)(√4 + √3) = (√4 + √3)^2 / 1 = (2+√3)^2 ∴　The given formula is √[(2+√3)^2] = 2+√3

[田中勉-cc]

分子、分母に+を掛ければ
分子は○の2乗となり、分母は2√2となり簡単に解けるのに。
何をしているの?