Question

Tính:

\(\sqrt{21+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)

Answer 1

Cách khác :

\(\sqrt{21+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}=\dfrac{\sqrt{36+2.6.\sqrt{6}+6}-\sqrt{36-2.6.\sqrt{6}+6}}{\sqrt{2}}=\dfrac{6+\sqrt{6}-6+\sqrt{6}}{\sqrt{2}}=\dfrac{2\sqrt{6}}{\sqrt{2}}=2\sqrt{3}\)

Answer 2

Đặt: \(A=\sqrt{21+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)

\(A^2=21+6\sqrt{6}-2\sqrt{\left(21+6\sqrt{6}\right)\left(21-6\sqrt{6}\right)}+21-6\sqrt{6}\)

\(A^2=42-2\sqrt{441-216}\)

\(A^2=42-2\sqrt{225}\)

\(A^2=42-30=12\)

\(\Rightarrow A=\sqrt{12}=2\sqrt{3}\)

Answer 3

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