Radicals (numbers and logic)
- Convert Radicals.
- Perform Operations on Radical Expressions.
- Solve Radical Equations.
UNIT PLAN (Lesson Schedule, Quiz and Exam Dates)
2023 Assessments:
Skills to review
Simplify Radicals
Convert entire radicals to mixed radicals, express mixed radicals in simplest form.
Skills to review
- Number Systems - categorize numbers into their systems based on their properties (natural, whole, integer, rational, irrational, real).
Simplify Radicals
Convert entire radicals to mixed radicals, express mixed radicals in simplest form.
- We will use multiplying skills to identify perfect square (perfect cube) factors. We will simplify our perfect squares (perfect cubes).
- We will multiply the natural number outside the radical by itself the number of times indicated by the index of the radical. We will find the product to create a new whole radical.
Add and Subtract Radicals.
Add and Subtract Radicals.
- When we add or subtract fractions we need to add and subtract like sizes - we need to have a common denominator.
- When we add or subtract radicals we need to add and subtract like sizes - we can only add and subtract like radicals.
- We often need to use our simplifying radical skills to make unlike radicals like radicals.
- Text Questions for practice: page 188 - 1,2,5,6,9,12,14-16,18,19
Multiply Radicals
SKILLS REVIEW
Divide Radicals
Dividing Radical Skills: Divide Skills and Answer Key
Radical Skills Review (from simplifying to dividing): old quiz and answer key
Text Questions (Extra Practice):
- Multiply - when we multiply polynomials, we multiply number x number, variable x variable. When we multiply radicals, we multiply whole number x whole number and radical x radical. After we multiply, we always look to simplify our new mixed radical to simplest terms.
- We will need to use the distributive property when we have multiplying with parenthesis.
SKILLS REVIEW
- Simplify, Add/Subtract & Multiply Radicals: Quiz 2020 and Answer Key
- Add, Subtract, Multiply and Simplify (old quiz): original and answer key
Divide Radicals
- Dividing - we want to have our answers with rational denominators (no radicals left in the bottom of the fraction).
- We look to divide whole number by whole number and radical by radical to simplify first.
- If we can not 'rationalize' the bottom of the fractions, we multiply the radical by itself... radical x radical skills. As we are working with fractions, what ever we multiply the bottom of the fraction by we need to multiply the top by too. If the top of the question is more than one term, we need to use the distributive property and multiply radical x radical for all the terms.
- Examples: 2019
- Divide Radicals: video lesson
Dividing Radical Skills: Divide Skills and Answer Key
Radical Skills Review (from simplifying to dividing): old quiz and answer key
Text Questions (Extra Practice):
- Multiply Questions, Page 198: 1,4,5,8
- Divide Questions, page 198: 3, 13, 14, 16
Solve Equations that contain a Radical
Equation and Dividing Skills:
- When we solve two step equations (like the ones we did for our starting puzzle today)we are always trying to get the variable by itself. To do this we need to know the lowest order of operation and do the opposite of that step first.
- Radical equations are solved with the same concept - we first need to isolate the radical expression using an opposite step or two. Once the radical is isolated we 'square both sides to solve for square root questions' or we 'cube both sides to solve for cube root questions'.
Equation and Dividing Skills:
- Dividing and Solve Equations Quiz 3.Sept2016: Original and Answer Key
Radicals with Variables
We use the same skills, just adding the layer of simplifying variables.
- Adding and Subtracting - only add and subtract like terms.
- Multiplying - multiply number by number and radical by radical.
- Dividing - we need to rationalize the denominators. With some dividing questions we can divide number by number and radical by radical... then simplify to get our answer. With more complicated dividing questions we need to multiply the top and bottom of the fraction by the radical in the denominator. Dividing may require us to use multiple skills to simplify.
Radical Skills Reviews:
Radical Skills:
Radical Skills:
- Unit Review One (Quiz 2. Sept 2018): Original and Answer Key
- Unit Review Two (Radicals Review): Original and Answer Key
- Unit Review Three (Radicals Worksheet): Original and Answer Key
- Extra Practice: Original and Answer Key
- 2022 Radical Quiz and Answer Key
- 2022 Radical Exams