How would you classify each of the following numbers: $\frac{\sqrt{12}}{2}, 1.5\cdot \sqrt{3}, \frac{3}{2}, \frac{2\sqrt{5}}{\sqrt{20}}$ ?

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Answer 1 · 2014-11-12T03:07:12

By simplifying a bit,

${sqrt{12}}/2={sqrt{2^2 cdot 3}}/{2}={2sqrt{3}}/2=sqrt{3}approx 1.7$

$1.5sqrt{3}=3/2sqrt{3}$

$3/2=1.5$

${2sqrt{5}}/{sqrt{20}}={2sqrt{5}}/{sqrt{2^2cdot5}}={2sqrt{5}}/{2sqrt{5}}=1$

Hence, we have

${2sqrt{5}}/{sqrt{20}} < 3/2 < {sqrt{12}}/2 < 1.5sqrt{3}$

I hope that this was helpful.

How would you classify each of the following numbers: \frac{\sqrt{12}}{2}, 1.5\cdot \sqrt{3}, \frac{3}{2}, \frac{2\sqrt{5}}{\sqrt{20}}\frac{\sqrt{12}}{2}, 1.5\cdot \sqrt{3}, \frac{3}{2}, \frac{2\sqrt{5}}{\sqrt{20}}?