Podcast
Questions and Answers
Simplify the radical expression: 14xy^{1/3} over 2x^{3/4} z^{-6}
Simplify the radical expression: 14xy^{1/3} over 2x^{3/4} z^{-6}
7x^{1/4} y^{1/3} z^{6}
What do the square root parent function and the cubed root parent function have in common?
What do the square root parent function and the cubed root parent function have in common?
The x and y intercepts are at the origin.
Solve the cubed root of x-16 minus 3=2.
Solve the cubed root of x-16 minus 3=2.
x=24
What is the domain and range of the function f(x)= square root of x+5 minus 3?
What is the domain and range of the function f(x)= square root of x+5 minus 3?
Signup and view all the answers
Simplify the radical expression: 5th square root of 4a^8 b^{14} c^5?
Simplify the radical expression: 5th square root of 4a^8 b^{14} c^5?
Signup and view all the answers
Solve square root of 2x+30 = x+3
Solve square root of 2x+30 = x+3
Signup and view all the answers
Identify the inverse of the equation y= square root of x+36.
Identify the inverse of the equation y= square root of x+36.
Signup and view all the answers
The functions f(x)= x-3 over 4 and g(x)= 4x+3 are inverses.
The functions f(x)= x-3 over 4 and g(x)= 4x+3 are inverses.
Signup and view all the answers
What is the function that is equivalent to: (4th square root of x^3)^5?
What is the function that is equivalent to: (4th square root of x^3)^5?
Signup and view all the answers
What expression is equivalent to: 1 over 4th square root of 5?
What expression is equivalent to: 1 over 4th square root of 5?
Signup and view all the answers
Study Notes
Radical Expressions
- Simplified radical expression: ( \frac{14xy^{1/3}}{2x^{3/4}z^{-6}} ) results in ( 7x^{1/4}y^{1/3}z^6 ).
- Fifth square root of ( 4a^8b^{14}c^5 ) simplifies to ( ab^2c^5\sqrt{4a^3b^4} ).
- Expression equivalent to ( (4^{\text{th}} \sqrt{x^3})^5 ) is ( x^{15/4} ).
- Equivalent expression for ( \frac{1}{4^{\text{th}} \sqrt{5}} ) is ( 5^{-1/4} ).
Functions and Properties
- Common features of square root and cubed root parent functions include intercepts at the origin.
- The domain and range of the function ( f(x) = \sqrt{x+5} - 3 ) are ( x \geq -5 ) and ( y \geq -3 ).
Solving Equations
- Solution to ( \sqrt[3]{x-16} - 3 = 2 ) gives ( x = 24 ).
- Solving the equation ( \sqrt{2x+30} = x+3 ) results in ( x = 3 ).
Inverse Functions
- The inverse of the equation ( y = \sqrt{x + 36} ) is expressed as ( y = (x - 6)^2 ).
- Functions ( f(x) = \frac{x - 3}{4} ) and ( g(x) = 4x + 3 ) are confirmed as inverses of each other.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers key concepts from Algebra 2 Chapter 6, including simplifying radical expressions and understanding the properties of root functions. Test your understanding of the domain, range, and solving equations involving radicals. Enhance your studies with this comprehensive flashcard set.
