Roots of Roots

Algebra Level 2

Find the value of \(x\) satisfying the equation \[ \sqrt{ 3\sqrt{x+5} - \sqrt{x-2} } = 3. \]

Details and assumptions

If the square root signs are not displaying clearly for you, the equation is equivalent to

\[ [3 ( x + 5 ) ^{\frac{1}{2}} - (x-2) ^\frac{1}{2} ]^\frac{1}{2} = 3. \]

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