# 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}}?

Nov 12, 2014

By simplifying a bit,

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

$1.5 \sqrt{3} = \frac{3}{2} \sqrt{3}$

$\frac{3}{2} = 1.5$

$\frac{2 \sqrt{5}}{\sqrt{20}} = \frac{2 \sqrt{5}}{\sqrt{{2}^{2} \cdot 5}} = \frac{2 \sqrt{5}}{2 \sqrt{5}} = 1$

Hence, we have

$\frac{2 \sqrt{5}}{\sqrt{20}} < \frac{3}{2} < \frac{\sqrt{12}}{2} < 1.5 \sqrt{3}$

I hope that this was helpful.