Which option correctly describes the nature of the expression (\sqrt{45}+\sqrt{80}-\sqrt{125})?

Irrational number

Simplify first: \(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), \(\sqrt{125}=5\sqrt{5}\). So the expression equals \(3\sqrt{5}+4\sqrt{5}-5\sqrt{5}=2\sqrt{5}\). Since \(\sqrt{5}\) is irrational, multiplying by the nonzero rational 2 yields an irrational number, so \(2\sqrt{5}\) is irrational. Why others are wrong: it cannot be rational because \(\sqrt{5}\) is irrational; it is not an integer; it is not zero because the coefficient 2 is nonzero. Exam tip: factor and combine like surd terms (same \(\sqrt{\;\;}\)) to simplify quickly.

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.