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1. 1. Radical Operations Totally Gnarly!
2. 2. Reducing Radicals <ul><li>Prime Factorization – the expression of a number as powers of its unique prime factors. </li></ul>EX There must be a factor of 2 in any even number. 45 is not prime so break it down. Careful 9 can become (3)(3). Finally combine all repeat primes.
3. 3. Reducing Radicals EX 2 Remember any number ending in 5 or 0 is divisible by 5. 343 hmm . . . Its not even and it doesn’t end in 5 or 0. Is it divisible by 3?
4. 4. Divisibility by 3 Test <ul><li>A number is divisible by 3 if and only if the sum of its digits is divisible by 3. </li></ul>EX Is divisible by 3? Since 27 is divisible by 3, 278154 is also divisible by 3.
5. 5. Reducing Radicals <ul><li>Is 343 divisible by 3? </li></ul>Great! And 49 can becomes (7)(7). Finally combine all repeat primes. NO It’s not divisible by 2, 3, or 5, let’s try 7.
6. 6. Reducing Radicals <ul><li>Ok, so what about those radicals! </li></ul>EX 1.) Prime factorize the radicand . The number under the radical 2.) Convert to fractional exponent form
7. 7. Reducing Radicals 3.) Distribute the fractional exponent. 4.) Simplify and rewrite any ½ powers in radical form. 5.) Simplify
8. 8. Reducing Radicals EX
9. 9. Adding Radicals <ul><li>Radicals are like fractions, only common radicals can be added or subtracted. </li></ul>EX EX Nothing can be done because the radicals do not have common radicands!
10. 10. Adding Radicals EX Wait isn’t this impossible! HA HA! Great! NO!
11. 11. Adding Radicals EX First we must reduce each radical! Prime Factorize! Can’t Simplify Combine Common Radicals
12. 12. Multiplying Radicals <ul><li>Radicals are again like fractions, you multiply the matching parts. </li></ul>Multiply the coefficients together. Multiply the radicands together.
13. 13. Multiplying Radicals <ul><li>A monomial times a binomial </li></ul>EX Don’t forget to simplify all radicals completely! Unlike Radicands CANNOT be added.
14. 14. Multiplying Radical <ul><li>A binomial times a binomial </li></ul>EX YOU MUST FOIL!!!!!
15. 15. Multiplying Radicals EX