Đặt \(A=\sqrt{17+4\sqrt{15}}-\sqrt{17-4\sqrt{15}}\) (A>0)
\(\Rightarrow A^2=(\sqrt{17+4\sqrt{15}}-\sqrt{17-4\sqrt{15}})^2\)
\(\Leftrightarrow A^2=17+4\sqrt{15}+17-4\sqrt{15}-2\sqrt{\left(17+4\sqrt{15}\right)\left(17-4\sqrt{15}\right)}\)
\(\Leftrightarrow A^2=34-2\sqrt{17^2-\left(4\sqrt{15}\right)^2}\)
\(\Leftrightarrow A^2=34-2\sqrt{49}\)
\(\Leftrightarrow A^2=34-2.7=20\)
\(\Rightarrow A=\sqrt{20}=2\sqrt{5}\)
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