Radical Escape

By: Austin Gugenheim

Radical Expressions

A radical expression contains three parts, a radical, a radicand, and the index.

  • The radicand is the number inside the radical symbol.
  • The index is the number that tells you what root you are looking for, in terms of the radicand.

Simplifying a Radical Expression

To simplify a radical expression, see if the radicand is a perfect square (or whatever your'e looking for).

If it's not a perfect square...

  1. Factor out the radicand.
  2. If you see any perfect squares, take the square root out.
  3. Repeat until you have no more perfect squares inside the radical symbol.


  1. √512
  2. √256 * 2
  3. √16 * 16 * 2
  4. 16√2

  1. √6 / 5
  2. √6 / √5
  3. √6 / √5 * √5 / √5
  4. √30 / √25
  5. √30 / 5

A Way to Remember

I found that an easy way to remember how to solve radical expressions is to think of them like jail cells. The index is the security level of the jail. The higher the index, the more people it takes in a group to get one person out. For example, if the index is four, it takes four of the same number to get one of the outside of the radical.