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Real Numbers — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsReal Numbers2 Marks
Question
Write whether $\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$ on simplification gives a rational or an irrational number.
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Answer

Let us simplify $\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$
$\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}=\frac{6\sqrt{5}+6\sqrt{5}}{2\sqrt{5}}$
$=\frac{12\sqrt{5}}{2\sqrt{5}}$
$=6$
6 is rational number.

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