Question

Write weather 2√45+3√20/2√5 on simplification gives a rational or irrational number.

Answer 1

Given , $\bold{\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}}$
$\bold{\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}} \\\\=\bold{\frac{2\sqrt{3\times3\times5}+3\sqrt{2\times2\times5}}{2\sqrt{5}}}\\\\=\bold{\frac{2.3\sqrt{5}+3.2\sqrt{5}}{2\sqrt{5}}}\\\\=\bold{\frac{12\sqrt{5}}{2\sqrt{5}}}=6$

Here you can see after simplifying we get 6 , according to definition of rational number [ a number , is in the form of P/Q, Q≠ 0 and P , Q ∈ I ] given number is rational number .

Hence, answer is rational number

Answer 2

I think it will help
2√45+3√20/2√5
2√3×3×5 + 3√2×2×5/2√5
2×3√5 + 3×2√5/2√5
6√5 + 6√5/2√5
12√5/2√5
6
hence it is rational number
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