Section 4 3 Terminology Entire Radical a radical

Section 4. 3

Terminology Entire Radical: a radical in the form Mixed Radical: a radical in the form

Part 1: Entire Radicals to Mixed Radicals 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

WHOAAAAA NELLY!!! Make sure your radical is in lowest terms!

HOW COULD WE HAVE AVOIDED THIS PROBLEM? 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

Simplifying with indices greater than 2

Part 2: Mixed Radicals to Entire Radicals 1. Square the number outside of the radical and write it under a radical sign. Try this one: 2. Multiply the two numbers together and put the answer under a radical sign.

More examples of mixed to entire radicals

Try this TOUGHIE! CONVERT FROM MIXED TO ENTIRE How can you rewrite 6 as a 4 th root? ? Just calculate 64 (6 x 6 x 6 x 6) and place it under the 4 th 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.

Please complete the remainder of your 4. 3 assignment. If finished, move on to the 4. 1 -4. 3 checkpoint in preparation for Thursday’s quiz!