Q.Find the square root of: \(33 - 4\sqrt{35}\) (a) \(\pm(\sqrt{7}-\sqrt{5})\) (b) \(\pm(2\sqrt{7}-\sqrt{5})\) (c) (3\sqrt{7}-\sqrt{5})\) (d) \(\pm(4\sqrt{7}-\sqrt{5})\)
Answer: B
\[ 33 - 4\sqrt{35} = 28 + 5 - 2 \cdot 2\sqrt{7} \cdot \sqrt{5} = (2\sqrt{7})^2 + (\sqrt{5})^2 - 2 \cdot 2\sqrt{7} \cdot \sqrt{5} = (2\sqrt{7} - \sqrt{5})^2 \] \[ \therefore \sqrt{33 - 4\sqrt{35}} = \pm (2\sqrt{7} - \sqrt{5}) \]
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