Simplifying radicals Rationalizing the denominatior UNIT 5: Radicals Simplifying radicals Rationalizing the denominatior

ROOTS Radical sign INDEX Radicand

Look for biggest perfect square that is a factor Simplify Square roots To simplify square roots. Find the biggest perfect square that divides evenly into the radicand. Look for biggest perfect square that is a factor What squared is 16? What squared is 36x2?

Adding square roots when adding/subtracting radicals you add/sub the coefficient or like radicals. (radicand has to be the same)

Multiplying radicals When multiplying two radicals together, multiply coefficients together & multiply radicands together.

Use “FOIL”, BOX, or whatever method you know to multiply Radical operations Use “FOIL”, BOX, or whatever method you know to multiply

Extra practice multiplying radicals

Simplify radicals Square root look for perfect squares(1,4,9,16,25,36…) Cube root look for perfect cubes(1,8,27,64,125…) Fourth root look for perfect fourth powers(1,16,81…) ~FOR EXAMPLE

Simplify Radicals Divide exponents by the index. Look for perfect square/cubes/fourths to be “pulled” out

Radical operations When add/sub radicals the radicand must be the same and you only add/sub number on outside. Multiply radicands together and outside number together When dividing

practice Radical operations(easy-hard) pg 371 #11-15 odd Simplify pg 371 #19-27 Pg 371 #37-41 odd

Rationalizing the denominator In most cases you don’t want to leave radical in the denominator. Rationalizing the denominator is a way to rewrite the expression without radicals in the denominator.