Actually this is a little urgent. While I was studying for the exam I encountered with this question. Neither my friends nor I could find the solution. It really seems easy though. Is there a short way or formula that I don't know?
2026-04-08 14:54:51.1775660091
If $a\sqrt{a} - 7\sqrt{a} = 2\sqrt{5}$ what is the value of $a-\sqrt{5a}$?
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If $t = \sqrt{a}$, your equation says $t^3 - 7 t - 2 \sqrt{5} = 0$. It's annoying to have that square root in the equation, so let $t = \sqrt{5} u$, and then it becomes $5 u^3 - 7 u - 2 = 0$. This factors as $(u+1)(5 u^2 - 5 u - 2)$, from which you can get the solutions. Caution: you probably don't want negative values of $t$.