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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