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Learn Radical Equations: Easy Steps & Fun Graphing!

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Learn Radical Equations: Easy Steps & Fun Graphing!
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Maria Hernandez

@mariahernandez

·

118 Followers

Follow

Top of the class Student

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

54

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

View

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))² = (4-7)², 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 f(x) is used to express relationships between variables and helps in graphical analysis.

Example: For f(x) = x-√(x-2), finding values where f(x) = 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

View

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-1) = 8 First square both sides: (√(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+5)+11 = 6, solve by isolating the radical first, then square both sides and solve for x.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Learn Radical Equations: Easy Steps & Fun Graphing!

user profile picture

Maria Hernandez

@mariahernandez

·

118 Followers

Follow

Top of the class Student

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

54

 

11th/12th

 

Algebra 2

2

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 content. It'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 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))² = (4-7)², 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 f(x) is used to express relationships between variables and helps in graphical analysis.

Example: For f(x) = x-√(x-2), finding values where f(x) = 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 content. It'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-1) = 8 First square both sides: (√(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+5)+11 = 6, solve by isolating the radical first, then square both sides and solve for x.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying