Radical Rules

Simplifying Radicals with Numbers

Vocabulary

• A radical is an expression containing a square root.

• √ is the radical symbol.

• The number goes inside of the symbol. This is the radicand. (example: √144)

• The index is the number on the corner of the symbol, telling you now many times the number must be squared. This amount is usually blank, which equals 2.

Product Rule

​When you have two terms that contain radicals, multiply them. Rewrite the radical as a product of the square number and another number.

3. Use the product rule.

4. Simplify the root of the perfect power.

1. Find the largest factor in the radicand. It has to be a perfect power of the index.

2. Rewrite the radicand as a product of the two factors.

General Steps to Solve

Example A: √45

Example B: √63

Homework Problems

A: √80 B: √48