D. Examples Using Prime Factorization and Cubed Roots

Step 1: Consider the factors of 81 (recall the Perfect Cube chart you completed in the Check Up).

81 × 1, 27 × 3, 9 × 9

Step 2: Identify the set of factors with the largest perfect cube.

Step 3: Express «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#1B4F66¨»«mn»81«/mn»«mn»3«/mn»«/mroot»«/math» as a product of its factors.

Step 4: Separate and give each factor its own root sign.

Step 5: The «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#1B4F66¨»«msup»«mn»3«/mn»«mn»3«/mn»«/msup»«mn»3«/mn»«/mroot»«mo mathcolor=¨#1B4F66¨»=«/mo»«mn mathcolor=¨#1B4F66¨»3«/mn»«/math», so rewrite the entire radical as a simplified mixed radical.