Radicals

Radicals

1. Adding and Subtracting Radicals

   • We will use the example √12 + √27.
     • √12 factors into √4 and √3. √4 then simplifies to 2, giving 2√3.
     • √27 factors into √3 and √3. This gives us 3√3.
     • These two come together, giving us 5√3. because √3 and √3 are like terms.

2. Simplifying Radicals

   • We will be using the example, √18.
     • We need to find a perfect square that goes into √18. The only perfect square that goes into it is 9. 9 is a perfect square and simplifies to 3. Therefore, we would put 3√2.

3. Multiplying Radicals

   • There are two ways to multiply radicals. First, you could multiply the radicals together, or factor them, and then multiply.
     • Multiplying Together
       • We will use the example, √72 * √12.
         • First, you would multiply 72 and 12, giving you √864. You would need to find factors that go into it.The largest factor would be √144. Since 144 * 6 is 864, you would put √144 * √6, giving us 12√6.
     • Multiplying After
       • We will use the example, √72 * √12.
         • First, you would find a factor that works for 72. In this case, we will be using 36. Since 36*2 is 73, it would become √36 and √2. √36 simplifies to 6√2. For 12, it would be 2√3. Multiply these together, and you get 12. these multiply together to get 12√6.