（\(\sqrt{\quad}\)５＋１）×\(\sqrt{\quad}\)（１０＋２\(\sqrt{\quad}\)５）／４
＝\(\sqrt{\quad}\)｛（\(\sqrt{\quad}\)５＋１）^2｝×\(\sqrt{\quad}\)（１０＋２\(\sqrt{\quad}\)５）／４
＝\(\sqrt{\quad}\)｛（６＋２\(\sqrt{\quad}\)５）（１０＋２\(\sqrt{\quad}\)５）｝／４
＝\(\sqrt{\quad}\)（６０＋３２\(\sqrt{\quad}\)５＋２０）／４
＝\(\sqrt{\quad}\)｛（８０＋３２\(\sqrt{\quad}\)５）／１６｝
＝\(\sqrt{\quad}\)（５＋２\(\sqrt{\quad}\)５）……（答）

残念ながら二重根号は開けません。
\(\sqrt{\quad}\)（６＋２\(\sqrt{\quad}\)５）ならば、\(\sqrt{\quad}\)５＋１と開けるのですが………。