Question
Insert five irrational number's between $2 \sqrt{3}$ and $3 \sqrt{5}$.
✓
Answer
We know that $2 \sqrt{3}=\sqrt{4 \times 3}=\sqrt{12}$ and $3 \sqrt{5}=\sqrt{9 \times 5}=\sqrt{45}$.
Thus, we have $\sqrt{12}<\sqrt{13}<\sqrt{14}<\sqrt{17}<\ldots \ldots<\sqrt{43}<\sqrt{44}<\sqrt{45}$
So, any five irrational numbers between $2 \sqrt{3}$ and $3 \sqrt{5}$ are:
$\sqrt{13}, \sqrt{14}, \sqrt{23}, \sqrt{37}, \sqrt{41}$
Thus, we have $\sqrt{12}<\sqrt{13}<\sqrt{14}<\sqrt{17}<\ldots \ldots<\sqrt{43}<\sqrt{44}<\sqrt{45}$
So, any five irrational numbers between $2 \sqrt{3}$ and $3 \sqrt{5}$ are:
$\sqrt{13}, \sqrt{14}, \sqrt{23}, \sqrt{37}, \sqrt{41}$
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