Question
Write the following in ascending order:$2 \sqrt{5}, \sqrt{3}$ and $5 \sqrt{2}$
✓
Answer
$2 \sqrt{5}=\sqrt{2^2 \times 5}=\sqrt{4 \times 5}=\sqrt{20}$
$\sqrt{3}=\sqrt{3} $
$5 \sqrt{2}=\sqrt{5^2 \times 2}=\sqrt{25 \times 2}=\sqrt{50}$
Since, $3<20<50$,
we have $\sqrt{3}<\sqrt{20}<\sqrt{50}$.
Hence, $\sqrt{3}<\sqrt{2}<5 \sqrt{2}$.
$\sqrt{3}=\sqrt{3} $
$5 \sqrt{2}=\sqrt{5^2 \times 2}=\sqrt{25 \times 2}=\sqrt{50}$
Since, $3<20<50$,
we have $\sqrt{3}<\sqrt{20}<\sqrt{50}$.
Hence, $\sqrt{3}<\sqrt{2}<5 \sqrt{2}$.
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