Write in ascending order : 6 5, 7 3, and 8 2 - Vidyadip

Question

Write in ascending order $: 6\sqrt5, 7\sqrt3, $ and $8\sqrt2$

✓

Answer

$ 6 \sqrt{ 5} =\sqrt{6^2 \times 5}=\sqrt{180}$
$ 7 \sqrt{ 3}=\sqrt{7^2 \times 3}=\sqrt{147}$
$ 8 \sqrt{ 2} =\sqrt{8^2 \times 2}=\sqrt{128}$
and $128<147<180$
$ \therefore \sqrt{128 } <\sqrt{147 } <\sqrt{ 180 }$
$ \Rightarrow 8 \sqrt{2 } <7 \sqrt{ 3 }<6 \sqrt{ 5}$

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