Radical Operations

Radical Operations Totally Gnarly!

Reducing Radicals ,[object Object],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.

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?

Divisibility by 3 Test ,[object Object],EX Is divisible by 3? Since 27 is divisible by 3, 278154 is also divisible by 3.

Reducing Radicals ,[object Object],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.

Reducing Radicals ,[object Object],EX 1.) Prime factorize the radicand . The number under the radical 2.) Convert to fractional exponent form

Reducing Radicals 3.) Distribute the fractional exponent. 4.) Simplify and rewrite any ½ powers in radical form. 5.) Simplify

Adding Radicals ,[object Object],EX EX Nothing can be done because the radicals do not have common radicands!

Adding Radicals EX Wait isn’t this impossible! HA HA! Great! NO!

Adding Radicals EX First we must reduce each radical! Prime Factorize! Can’t Simplify Combine Common Radicals

Multiplying Radicals ,[object Object],Multiply the coefficients together. Multiply the radicands together.

Multiplying Radicals ,[object Object],EX Don’t forget to simplify all radicals completely! Unlike Radicands CANNOT be added.

Multiplying Radical ,[object Object],EX YOU MUST FOIL!!!!!

Radical Operations

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Radical Operations