Question

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

Answer 1

I HOPE IT WILL HELP U
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
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PLS MARK IT AS BRAINLIST

Answer 2

Answer: It is a rational number.

Step-by-step explanation:

Since we have given that

$\dfrac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$

Since we can write :

√45=3√5

and

√20 = 2√5

So, it becomes,

$\dfrac{2\times 3\sqrt{5}+3\times 2\sqrt{5}}{2\sqrt{5}}\\\\=\dfrac{6\sqrt{5}+6\sqrt{5}}{2\sqrt{5}}\\\\\\=\dfrac{12\sqrt{5}}{2\sqrt{5}}\\\\\\=\dfrac{12}{2}\\\\\\=6$

so, it is a rational number.