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

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

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Answer 1 · 2014-11-12T03:07:12

By simplifying a bit,

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

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

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

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

Hence, we have

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

I hope that this was helpful.

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

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