Question

write whether 2√45+3√20by 2√5 on simplifying gives a rational or an irrational

Answer 1

Step-by-step explanation:

Given , \bold{\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}}

2

5

2

45

+3

20

\begin{lgathered}\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\end{lgathered}

2

5

2

45

+3

20

=

2

5

2

3×3×5

+3

2×2×5

=

2

5

2.3

5

+3.2

5

=

2

5

12

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