Explain how to use a number's greatest square factor to write the square root of that number in simple radical
form.

Let’s use an example, root40

Now, let’s find all the factors of 40 .

1, 2, 4, 5, 8, 10, 20, 40.

Now, let’s pick the greatest factor that is also a perfect square, meaning that if we took the square root of it, we would get a nice whole number.

In this case, the greatest factor that is a perfect square is 4.

Now, we can write the radical as

root4 • root10

Because 4 • 10 is 40, our original radical

Now we can simplify this to 2•root10.