Radicals

Radicals

1. Simplify Radical Expressions

   • When you are simplifying Radical Expressions, you start off with listing the factors of the number inside the radical. Use a pair of numbers, where at least one is a perfect square.
     • √45y^4 factors of 45: 45 & 1, 9 & 5 use 9&5 because 9 is a perfect square.
       • The square root of 9 is 3. So put the 3 on the outside and leave the 5 in the radical sign. Bring the y^4 back. 3√5y^4
         • 3√5y^4 √y^4 = y² You're left with 3√5y²

2. Add and Subtract Radical Expressions

   • When adding or subtracting radical expressions, you start off by simplifying if it's possible.
     • Step 1: 5√3 + √12 √12=√4*3=2√3
     • Then add the numbers outside of the radicals.
       • Step 2: 5√3+2√3 =7√3
   • *** If the number inside the radical is the same, don't add/subtract it, just leave it as it is. However, do add/subtract the numbers outside of the radical.
     • Ex: 2√5+3√5 5√5

3. Multiply Radical Expressions

   • When multiplying Radical Expressions, you multiply the number inside the radical and the number outside of the radical.
     • Step 1: 8√3 * 9√27 72√81
     • Simply if it's possible.
       • Step 2: 72 √81=9 72*9=648