Consider the given set of numbers.
{-6,6^3,1.6,sqrt(6)}
In order to compare them, we will rewrite them all to be in decimal form. The numbers -6 and 1.6 are already in decimal form, so we do not need to change these numbers at all. Let's start by calculating 6^3.
6^3=216
Now, since it is not a perfect square, we can approximate sqrt(6) using a calculator:
sqrt(6)=2.449489...
Finally, let's compare them. We can see that ordering from the least to the greatest gives us:
{-6,1.6,2.449489...,216}
⇓
{-6, 1.6, sqrt(6), 6^3 }
Alternative Solution
A different way of thinking...
We could have arrived to the same conclusion if we had thought about the numbers for a while. First of all, -6 is the only negative number, so it must be the least. Also, we know that numbers raised to an integer power grow very fast, it is no surprise that 6^3 is the greatest. Finally, to decide which is greater between 1.6 and sqrt(6) we can notice that
sqrt(6) > sqrt(4)=2
Since sqrt(4) is greater than 1.6, it must be the case that sqrt(6) > 1.6. The ordering once again gives us:
{-6, 1.6, sqrt(6), 6^3 }
