Which option is the value of (\sqrt{2}\times(\sqrt{18}-\sqrt{8}))?

(2)

The governing concept is simplifying each surd by removing perfect-square factors and then multiplying. We have \sqrt{18}=\sqrt{9\cdot2}=3\sqrt{2} and \sqrt{8}=\sqrt{4 aimes2}=2\sqrt{2}. Therefore the bracket becomes 3\sqrt{2}-2\sqrt{2}=\sqrt{2}. Multiplying by the outside factor gives \sqrt{2}\cdot\sqrt{2}=2, because \sqrt{a}\sqrt{a}=a for a non-negative a. Thus option A is correct. Option D is the unsimplified product, while B and C arise from incorrect multiplication or failure to subtract like surd terms correctly. The result is rational even though the original expression contains irrational factors.

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