Which is greater between ( \sqrt{2} ) and ( \sqrt{3} )?

Correct answer: ( \sqrt{3} )

Direct answer: Option B, \(\sqrt3\). Both 2 and 3 are positive, and the square-root function preserves order for positive numbers. Since \(3>2\), we get \(\sqrt3>\sqrt2\). A numerical check also helps: \(\sqrt2\) is about 1.41, while \(\sqrt3\) is about 1.73. Option A, \(\sqrt2\), is not correct because it is the smaller root. Option B is correct because the number under its root, 3, is larger than the number under the other root, 2. Option C, both are equal, is wrong because equal non-negative square roots would have equal squares, but their squares are 2 and 3, which are different. Option D, both are not real, is wrong because the square roots of positive numbers are real numbers. A useful safe method is to square both positive quantities: comparing \(\sqrt2\) and \(\sqrt3\) is equivalent to comparing 2 and 3. Remember: for non-negative radicands, the larger radicand has the larger square root.