Question

which list shows these diagonal lengths in order from greatest to least

Answer 1

The values we have for the diagonal length are:

$\begin{gathered} 4\sqrt[\square]{13} \\ 14\frac{2}{5} \\ 14.33 \end{gathered}$

To compare them and see which of them is greatest, we need to convert all of them to decimal numbers.

For the first number:

$4\sqrt[=]{13}=4\cdot3.6055=14.422$

for the second number:

$14\frac{2}{5}=14.4$

And the third number is already in decimal form:

$14.33$

We arrange them from greatest to least in decimal form:

$14.422,\text{ 14.4, 14.33}$

And then we go back and substitute the original numbers:

$4\sqrt[]{13},14\frac{2}{5},14.33$

Answer:

$4\sqrt[]{13},14\frac{2}{5},14.33$