Radicals

Radicals

1. Multiplying Radicals

   • Multiplying Radicals is not as hard as it might seem. When multiplying Radicals just multiply the numbers inside the radical symbol.
   • Step2: After you have multiplied , simplify your anwer
   • An Example: √3 x V12 = √36. Then I would simplify √36= 6 √
   • If there are numbers outside the radical. Multiply the number outside by the other number outside the Radical. Then multiply the numbers inside the radical. And then simplify
     • Example : 2 √3 x 8 √3 = 16 √9. Simplify and the answer is 4 √3

2. Adding and Subtracting Radicals

   • When adding radicals you must follow a very important rule. Only add radicals With like terms
     • If the number of inside the radical symbol is the same as the other's number inside the symbol. It is a like term
       • Example: 2 √ 4 + 2 √3. These are not like terms. Even if both of these radicals contain twos on the outside of the radical symbol., because the numbers inside the radical symbol are 3 and 4 , which means they are different. If they are not like terms they cannot be combined
         • A correct form of combining radicals would be something like this. 2 √4 + 6 √4 = 8 √4

3. Simplifying Radicals

   • A radical is at it's simplest form when the radicand ( number/variable inside the radical symbol) has no more square factors
     • √33 for example has no perfect square factors. 33's factors are 11 and 3. Neither of these are a perfect square root. Therefore √33 is in it's original form
     • Another example is √18. It's Factors are 9 and 2. But 9 can be further simplified since it's a perfect square root, simplifying to 3. 2 cannot be simplified further more so t stays inside the radical. The answer is 3 √2
   • look for factors that are perfect squares or have perfect squares
   • Don't panic when you see a radical with variables. Here is an example on how to deal with variables.
     • You would pretty much do the same with variables as what you do with numbers. √36m^4..So simplify the 36 first and this would be equal to 6. Now the m^4 can be simplified because the perfect square of 4 is 2. Since you have simplified these terms they would go outside the radical symbol. Your answer would be 6m^2 √.