G. Converting a Mixed Radical to an Entire Radical

Recall the relationship between a radical with a perfect square radicand and its Whole Number equivalent.

For example, consider , as shown below.

Example 1

Let's analyze some more square roots. Do you see any patterns?

Example 2

Example 3

There are several patterns:

  • Squared numbers are apparent: 2 × 2, 3 × 3, 4 × 4
  • Another way to represent squared numbers is with an exponent of
  • The square root and the exponent 2 undo each other.