# How would you order the number from least to greatest: \frac{\sqrt{6}}{2}, \frac{61}{50}, \sqrt{1.5}, \frac{16}{13}?

Dec 25, 2014

I assume we may not use a calculator, otherwise it's quite simple.

Let's look at the first: this can be written as:
$\frac{\sqrt[2]{6}}{\sqrt[2]{4}} = \sqrt[2]{\frac{6}{4}} = \sqrt[2]{1.5}$ is the same as number three.

number two: $\frac{61}{50} = 1 + \frac{11}{50} = 1 + \frac{22}{100} = 1.22$

number four: $\frac{16}{13} = 1 + \frac{3}{13}$

These numbers are all close together (I did check with a calculator) so I think this one cannot be solved without a calculator.

The correct order is:
$\frac{61}{50} = 1.22$ then

$\frac{\sqrt[2]{6}}{2}$ and $\sqrt[2]{1.5}$ (both$= 1.2247 \ldots$) then

$\frac{16}{13} = 1.2307 \ldots$

I'm sorry I can't do this by reasoning alone, but I hope this helps.

Dec 26, 2014

I don't think my answer was correct.