P (√3, 5) = P ([tex]x_{1}, y_{1}[/tex]) ; Q (5√3, √5) = Q ([tex]x_{2}, y_{2}[/tex])
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[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1})^{2}}\\\\d = \sqrt{(5\sqrt{3} - \sqrt{3} )^{2} + (\sqrt{5} - 5)^{2}}\\d = \sqrt{(\sqrt{3} (5 - 1))^{2} + ((\sqrt{5}) ^{2} - 2. 5. \sqrt{5} + 5^{2})}\\d = \sqrt{(3 . (4)^{2}) + 5 - 10\sqrt{5} + 25}\\d = \sqrt{48 + 5 - 10\sqrt{5} + 25}\\d = \sqrt{78 - 10\sqrt{5}}\\[/tex]
