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Consider a minimal example:

FullSimplify[Sqrt[2/15 (7 + 3 Sqrt[5])]]

This will turn out nothing. On the other hand, the expression can be indeed simplified, since

Sqrt[2/15 (7 + 3 Sqrt[5])] == Sqrt[3/5] + 1/Sqrt[3]

One should expect FullSimplify will simplify the left expression to the right expression, but it does not. I have this expression

128/25 Sqrt[559/5 - 248/Sqrt[5]] - 36352/25 Sqrt[5939/5 + 2656/Sqrt[5]] - 8336/15 Sqrt[9074/5 + 4058/Sqrt[5]] - 64 Sqrt[3/5 (9 - 4 Sqrt[5])] - 144/5 Sqrt[3 (9 - 4 Sqrt[5])] + (2263 Sqrt[3 - Sqrt[5]])/240 - 16 Sqrt[6/5 (3 - Sqrt[5])] - (4 Sqrt[3 + Sqrt[5]])/15 - 304/75 Sqrt[2/5 (5 + Sqrt[5])] - 136/75 Sqrt[2 (5 + Sqrt[5])] - 3/10 Sqrt[9/2 + 2 Sqrt[5]] - 2848/15 Sqrt[331 + 148 Sqrt[5]] + 6368/75 Sqrt[1655 + 740 Sqrt[5]] + 8/75 Sqrt[2330 + 1042 Sqrt[5]] + 16/375 Sqrt[2 (5825 + 2605 Sqrt[5])] + 16256/25 Sqrt[5939 + 2656 Sqrt[5]] + 3728/15 Sqrt[9074 + 4058 Sqrt[5]] + 483/4 Sqrt[930249/10 + 41602 Sqrt[5]]

How to simplify it into just sum of square roots as in the previous case?

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    $\begingroup$ Try ResourceFunction["RadicalDenest"][Sqrt[2/15 (7 + 3 Sqrt[5])]]. Your longer equation simplifies to $\frac{1}{480} \left(8836429 \sqrt{2}-10752 \sqrt{3}+3954999 \sqrt{10}\right)$. There's something about this recently at community.wolfram.com but I can't find it at the moment. $\endgroup$
    – JimB
    Dec 17, 2020 at 16:18
  • 4
    $\begingroup$ @JimB Wolfram Community post. $\endgroup$
    – Rohit Namjoshi
    Dec 17, 2020 at 17:01

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