Section 4.3 Terminology Entire Radical: a radical in the form Examples : 35 , x 68 Mixed Radical: a radical in the form a x Examples : 3 5 , − 4 21 Part 1: Entire Radicals to Mixed Radicals 72 = 36 × 2 =6 2 1. Find the LARGEST perfect square that is a factor of the radicand. 2. Rewrite the radicand as a product of its largest square and another number. 3. Take the square root of the perfect square and write the answer as a mixed radical Remember the Perfect Squares: 1, 4 , 9, 16, 25, 36, 49, 64, 81, 100… Examples 50 = 5 2 25 • 2 150 = 5 6 25 • 6 288 = 12 2 144 • 2 48 = 2 12 4 • 12 WHOAAAAA NELLY!!! 48 = 2i 12 4 i 12 4i 3 = 2i2i 3 = 4i 3 Make sure your radical is in lowest terms! HOW COULD WE HAVE AVOIDED THIS PROBLEM? 48 = 4i 3 16 • 3 We should have written the radicand as a product of its largest square and another number. Not just any square! Both methods will get you full marks, as long as your final answer has the radicand in its lowest terms! More mixed radicals that can be further reduced ☺ 6 27 = 6 9 × 3 = 6× 3 3 = 18 3 4 20 = 4 4 × 5 = 4× 2 5 = 8 5 5 80 = 5 16 × 5 = 5× 4 5 = 20 5 Simplifying with indices greater than 2 3 3 4 54 = 27 × 2 3 =3 2 3 16 = 8× 2 =2 2 80 = 16× 5 =2 5 3 4 3 4 Part 2: Mixed Radicals to Entire Radicals 3 6 = 9× 6 = 54 Try this one: 4 5 = 16 × 5 = 80 1. Square the number outside of the radical and write it under a radical sign. 2. Multiply the two numbers together and put the answer under a radical sign. More examples of mixed to entire radicals ☺ 6 27 = 36 × 27 = 972 3 2 2 = 8× 2 = 16 5 2 = 25 × 2 = 50 3 3 3 Try this TOUGHIE! CONVERT FROM MIXED TO ENTIRE How can you rewrite 6 as a 4th root?? 4 6 5 = 1296 × 5 4 4 = 6480 4 Just calculate 64 (6x6x6x6) and place it under the 4th root sign! REMEMBER! If you are not confident that this is the answer, always check by evaluating both numbers in your calculator. They should match. See the end of lesson 4.1 for more details.