Here is a typical square root:
This is an irrational number, since there is no rational number that will multiply by itself to give 32.
In fact, the square root of 32 has this value:
This is an irrational number. It goes on forever, and there is never a complete repeating pattern.
This means that if you want to use the square root of 32 in a calculation, you will have to round it.
For example, you might choose to round the square root of 32 to about 5.7, or perhaps 5.657
However, in order to work with it, you will have to make a decision about how to round it.
Suppose, though, you were working with a formula. Here's an example:
You have just come up with this formula, and want it to be used to find the height of something.
The problem occurs if you decide to evaluate the square root of 32, and round it.
Without knowing who will be using the formula, or how big the value of t will be, there is no way you can make a decision about how much to round the square root of 32!
For example, if you decide to round it to 1 decimal place, using 5.7, and someone using the formula enters a value of 973 for t, their final answer will not be as accurate as if you'd used 5.657
You have no way of knowing in advance how much to round the square root!
You could leave the square root of 32 untouched. But we're supposed to always make expressions as simple as possible.
A better solution to this dilemma is to simplify the square root of 32, but not evaluate it.
We're going to show you how to simplify a square root.