Simplifying, Adding/Subtracting & Multiplying Radicals

Simplifying, Adding/Subtracting & Multiplying Radicals

1. Simplify radical expressions

   • To simplify a radical expression you need to find perfect square that will go into your radical.
     • square root of 125
       • 25 and 5 go into 125. 25 is a perfect square. The square root of 25 is 5 so it goes outside the radicand.
         • This leaves you with 5 square root 5.

2. Add and Subtract radical expressions

   • When you subtract and add radicals you need to simplify first.
     • If the radicals can't be simplified, simply leave it as is, unless they have like bases, in which case you should add the numbers outside and keep the same base.

3. Multiply Radical expressions

   • Multiplying radicals can be done in many ways. I will mention two. You can either multiply the radicals first (like normal, multiply the bases and the outside numbers) or you can simplify the radicals.
     • Multiplying first probably looks simpler but you will need to work with bigger numbers.
     • Depending on the problem simplifying may take more steps, but an advantage is working with smaller numbers.

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