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Number Systems — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumber Systems1 Mark
Question
State whether the following statements are true or false? Justify your answer. $\frac{\sqrt{15}}{\sqrt{3}}$ is written in the form $\frac{\text{p}}{\text{q}}, \text{ q}\neq0$ and so it is a rational number.
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Answer

False. Solution: $\frac{\sqrt{15}}{\sqrt{3}}=\frac{\sqrt{5\times3}}{\sqrt{3}}=\frac{\sqrt{5}\times\sqrt{3}}{\sqrt{3}}=\sqrt{5},$ which is an irrational number.

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