Unit 4 Lesson 1.notebook
September 28, 2016
Math 2201: Unit 4 Lesson 1
Review of Radicals
tells us which root to take
ie. square root, cube root, etc.
the number that we are taking
the root of
1
Unit 4 Lesson 1.notebook
September 28, 2016
Principal vs. Secondary Square Root
Example: Determine the value of x:
3
4
Which would be more appropriate to use as your answer: the primary or the secondary square root?
2
Unit 4 Lesson 1.notebook
September 28, 2016
Entire vs. Mixed Radicals
Entire Radical: a radical that is not multiplied by any number other than 1. Mixed Radical: a radical that is multiplied a number other than 1. Examples: Tell whether the following represent entire or mixed radicals.
Review: Simplifying Radicals
To determine whether a radical can be simplified, use your calculator to take the square/cube/fourth/etc. root (whichever is required). If the answer works out to be a whole number, then you simply need to state that answer.
Example: Express each radical in simplest form.
3
Unit 4 Lesson 1.notebook
September 28, 2016
Sometimes the radicand may not be a perfect square/cube, etc. In these cases, when we take the root using a calculator, we get a decimal number instead of a whole number. In these cases, we may be able to break the radical down into a mixed radical. There are two methods for doing this: (1) finding the largest perfect square/cube, etc. factor of the radicand and (2) the factor tree method
...
Method 1
: Finding the Largest Perfect Square/Cube, etc. Factor of the Radicand
Example: Simplify Make a list of perfect square numbers by squaring the natural numbers...
...
...
Pick the largest perfect square that can be divided evenly into the radicand.
4 is the largest perfect square that will go into 20
write the square root as a product
of roots (with the perfect square factor written first)
Example: Simplify
Make a list of perfect cube numbers by cubing the natural numbers...
Pick the largest perfect cube that can be divided evenly into the radicand.
8 is the largest perfect cube that will go into 16.
4
Unit 4 Lesson 1.notebook
September 28, 2016
Method 2: Factor Tree Method
5
Unit 4 Lesson 1.notebook
September 28, 2016
Examples: Using the method of your choice, simplify the following.
1.
2. 6
Unit 4 Lesson 1.notebook
September 28, 2016
QUESTIONS: Using the method of your choice, simplify the following.
7