What is the value of \(\dfrac{\sqrt{45}}{\sqrt{5}}\)?

3

Solution: \(\dfrac{\sqrt{45}}{\sqrt{5}}=\sqrt{\dfrac{45}{5}}=\sqrt{9}=3\). Use the property \(\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b}}\). Option B (9) reflects a common mistake of removing the radical incorrectly and treating the expression as \(45/5=9\) without taking the square root; note that \(9\neq\sqrt{9}\). Options C and D are wrong because they result from incorrect cancellation or ignoring the denominator. Exam tip: when dividing square roots, combine under a single radical first (simplify \(a/b\)) and then take the square root to avoid algebraic errors.

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