Questions and Answers
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?
The x and y intercepts are at the origin.
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?
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Simplify the radical expression: 5th square root of 4a^8 b^{14} c^5?
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Solve square root of 2x+30 = x+3
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Identify the inverse of the equation y= square root of x+36.
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The functions f(x)= x-3 over 4 and g(x)= 4x+3 are inverses.
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What is the function that is equivalent to: (4th square root of x^3)^5?
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What expression is equivalent to: 1 over 4th square root of 5?
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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.
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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.
