A ladder is leaning against a wall. The base of the ladder is 10 feet away from the base and forms a 60° angle with the ground. What is the length of ladder to the nearest foot?

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Step-by-step explanation:

Here are some counter examples to disprove the original claim.

The decimal values are approximate.

All of those values are known as transcendental numbers. These are a class of numbers where we cannot write them as a root of some other number. It's similar to the idea how irrational numbers cannot be written as a ratio of two integers. All transcendental numbers are irrational, but not the other way around.

So in short, it is possible to have an irrational number where it's not a radical.