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Learn Radical Equations: Easy Steps & Fun Graphing!

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Maria Hernandez

6/30/2023

Algebra 2

Solving Radical Solutions

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Algebra 2

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Transformations

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Graphs of Square and Cube Root Functions

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Radical Functions & Their Graphs

Learn Radical Equations: Easy Steps & Fun Graphing!

Solving radical equations requires careful attention to detail and systematic problem-solving approaches. This comprehensive guide covers essential techniques for solving various types of radical equations with step by step examples and methods for checking extraneous solutions in radical equations.

  • Learn systematic approaches to solve equations containing square roots and other radicals
  • Master the technique of isolating radicals and squaring both sides
  • Understand the importance of checking solutions using graphing functions with Desmos
  • Practice with diverse examples ranging from simple to complex radical equations
  • Identify and eliminate extraneous solutions through verification
...

6/30/2023

56

Solving Radical Solutions Ex. √ 5x-1 = 8 (√5x-1)²=8² Sx-I:64 +1 +1 5x = 65 5X = 4653 13 Ex. √3x-2-5 3 X = = 0 +5 +5 ·2 = 5² √3x-2 3x-2=25 +2

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Page 2: Advanced Applications and Solution Verification

This page delves into more complex radical equations and introduces the use of Desmos for solution verification. It emphasizes the importance of checking solutions and understanding the relationship between algebraic and graphical approaches.

Example: Solving √√(2x+1√√(2x+1)² = 4−74-7², which requires careful attention to multiple radicals and proper algebraic manipulation.

Highlight: Using Desmos graphing calculator provides a visual method to verify solutions and identify points of intersection.

Vocabulary: Function notation fxx is used to express relationships between variables and helps in graphical analysis.

Example: For fxx = x-√x−2x-2, finding values where fxx = 4 requires both algebraic and graphical approaches.

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Subjects

Algebra 2

Transformations

Graphs of Square and Cube Root Functions

Radical Functions & Their Graphs

 

Algebra 2

•

56

•

Jun 30, 2023

•

2 pages

Learn Radical Equations: Easy Steps & Fun Graphing!

user profile picture

Maria Hernandez

@mariahernandez

Solving radical equations requires careful attention to detail and systematic problem-solving approaches. This comprehensive guide covers essential techniques for solving various types of radical equations with step by step examples and methods for checking extraneous solutions in radical equations.... Show more

Solving Radical Solutions Ex. √ 5x-1 = 8 (√5x-1)²=8² Sx-I:64 +1 +1 5x = 65 5X = 4653 13 Ex. √3x-2-5 3 X = = 0 +5 +5 ·2 = 5² √3x-2 3x-2=25 +2

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Page 2: Advanced Applications and Solution Verification

This page delves into more complex radical equations and introduces the use of Desmos for solution verification. It emphasizes the importance of checking solutions and understanding the relationship between algebraic and graphical approaches.

Example: Solving √√(2x+1√√(2x+1)² = 4−74-7², which requires careful attention to multiple radicals and proper algebraic manipulation.

Highlight: Using Desmos graphing calculator provides a visual method to verify solutions and identify points of intersection.

Vocabulary: Function notation fxx is used to express relationships between variables and helps in graphical analysis.

Example: For fxx = x-√x−2x-2, finding values where fxx = 4 requires both algebraic and graphical approaches.

Solving Radical Solutions Ex. √ 5x-1 = 8 (√5x-1)²=8² Sx-I:64 +1 +1 5x = 65 5X = 4653 13 Ex. √3x-2-5 3 X = = 0 +5 +5 ·2 = 5² √3x-2 3x-2=25 +2

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Fundamental Techniques for Solving Radical Equations

The first page introduces core concepts and methods for solving radical equations through multiple worked examples. The process typically involves isolating the radical term and squaring both sides to eliminate the radical.

Example: Solving √5x−15x-1 = 8 First square both sides: √(5x−1√(5x-1)² = 8² Then solve: 5x-1 = 64, leading to x = 13

Highlight: When solving radical equations, always check your answers as squaring both sides can introduce extraneous solutions.

Definition: Extraneous solutions are apparent solutions that don't actually satisfy the original equation when checked.

Example: For the equation √2x+52x+5+11 = 6, solve by isolating the radical first, then square both sides and solve for x.

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user