Multiple Choice Question (MCQ)
Which of the following is equal to \sqrt{9-6\sqrt{2} } +\sqrt{9+6\sqrt{2} }
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×
3\sqrt{2}
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✓
2\sqrt{6}
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×
\dfrac{7\sqrt{2} }{2}
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×
3\sqrt{3}
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×
6
Answer
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\sqrt{9-6\sqrt{2} } +\sqrt{9+6\sqrt{2} }
=\sqrt{(\sqrt{9-6\sqrt{2} } +\sqrt{9+6\sqrt{2} })^2}
=\sqrt{9-6\sqrt{2}+9+6\sqrt{2}+2\sqrt{9-6\sqrt{2}}\sqrt{9+6\sqrt{2}}}
=\sqrt{18+2\sqrt{81-72}}
=\sqrt{24}
=2\sqrt{6}