Simplify = 2 = 4 = 5 = 10 = 12

Simplifying Radical Expressions A radical expression is in its simplified form if it contains no perfect squares as factors.

Objective - To simplify rational and irrational square roots. List of Perfect Squares

Objective - To simplify irrational roots. Example: Check using a calculator!

Simplify. To simplify the number by hand must have a perfect square factor. No perfect square factors Can’t be simplified

Simplify each irrational root. 1) 4) 2) 5) 3) 6)

Simplify. Perfect square

Simplify each irrational root. 1) 4) Already Simplified 2) 5) 3) 6)

Ex. 1 Simplify

Ex. 2 Simplify

Radicals with Variables To simplify radicals with variables: divide even exponents by 2; for odd exponents, pull out the largest even exponent, take the square root of that, and leave the remainder under the radical.

Radicals with Variables Ex. 10 Even Radicals with Variables      

Radicals with Variables Ex. 11 Odd Radicals with Variables      

+ Combine Like Radicals Miller Miller To combine radicals: combine the coefficients of like radicals. They must have the same last name.

Ex. 3 Simplify Your Turn

Ex. 4 Simplify, then combine.

Ex. 5 Simplify, then combine.

Example The greatest perfect square factor of 96a4b is 16a4. Use the product rule of square roots to separate the factors into two radicals. Find the square root of 16a4 and leave 6b in the radical. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example Solution The greatest perfect square factor of 32x5 is 16x4. Use the product rule of square roots to separate the factors into two radicals. Find the square root of 16x4 and leave 2x in the radical.

Multiply Radicals * To multiply radicals: multiply everything, then simplify.

Ex. 6 Multiply, then simplify.

Squared and Square Root Cancel Ex. 7 Squared and Square Root Cancel

Dividing Radicals To divide radicals: reduce or divide what you can and rationalize the denominator. A square root CANNOT be in the denominator.

Reduce or divide, then rationalize. Ex. 8 Reduce or divide, then rationalize.

Ex. 9