Radicals

Radicals

1. Simplify radical expressions

   • Ex: √125
     • First, you would find all the factors of the number being square rooted.
     • Factors: 1, 5, 25, 125
       • Second, you would look for a factor that is a perfect square.
       • √125 = √25 x √5 = ±5 x √5
         • 5√5
           • Since 25 has been square rooted the 5 has to be on the outside of the square root symbol.
   • If an exponent is involved you would multiply the exponent by 1/2

2. Add and Subtract Radical expressions

   • Ex: 2√12 + √27
     • First, you simplify radicals
     • √12 = √4 *√3 = 2√3 √27 = √9 * √3 = 3√3
       • 2 * 2√3 + 3√3
         • Then, you combine like radicals
         • 4√3 + 3√3
           • 7√3

3. Multiply Radical expressions

   • Ex: √18 * √16
     • First, you multiply straight through
       • Then, you simplify radicals
     • √288 = √144 * √2 = 12 * √2
       • 12√2