Which expression is equivalent to startroot 120 x endroot – Which expression is equivalent to √(120x)? Exploring this mathematical concept, this article delves into the intricacies of square roots and equivalent expressions, providing a comprehensive understanding of their usage and applications.
This article will delve into the mathematical intricacies of √(120x), examining its equivalent expressions and their applications. By understanding the order of operations, the meaning of the radical symbol, and the properties of equivalent expressions, we can effectively solve equations involving √(120x) and appreciate its significance in mathematical operations.
Equivalent Expressions to ‘startroot 120 x endroot’
The mathematical expression ‘startroot 120 x endroot’ represents the principal nth root of 120x, where n is the index of the radical. In other words, it is the positive value of x such that x n= 120x. For example, ‘startroot 120 x endroot’ is equivalent to x = 3√(120x).
Equivalent Expressions, Which expression is equivalent to startroot 120 x endroot
- ‘startroot 120 x endroot’ is equivalent to 3√(120x)
- ‘startroot 120 x endroot’ is equivalent to (120x) 1/3
- ‘startroot 120 x endroot’ is equivalent to e (ln(120x)/3)
These expressions are all equivalent because they represent the same value for x. For example, if x = 2, then ‘startroot 120 x endroot’ = 3√(120(2)) = (120(2)) 1/3= e (ln(120(2))/3)= 6.
Use in Solving Equations
‘startroot 120 x endroot’ can be used to solve equations. For example, to solve the equation ‘startroot 120 x endroot’ = 6, we can cube both sides of the equation to get (startroot 120 x endroot’) 3= 6 3. This gives us x = 2.
Table of Related Expressions
| Expression | Equivalent Expressions |
|---|---|
| ‘startroot 120 x endroot’ | 3√(120x), (120x)1/3, e(ln(120x)/3) |
| 3√(120x) | ‘startroot 120 x endroot’, (120x)1/3, e(ln(120x)/3) |
| (120x)1/3 | ‘startroot 120 x endroot’, 3√(120x), e(ln(120x)/3) |
| e(ln(120x)/3) | ‘startroot 120 x endroot’, 3√(120x), (120x)1/3 |
The expressions in this table are all equivalent because they represent the same value for x.
Graphical Representation
The graphical representation of ‘startroot 120 x endroot’ is a curve that passes through the point (0, 0) and increases without bound as x increases. The graph of ‘startroot 120 x endroot’ can be used to visualize the value of the expression for different values of x.
Question & Answer Hub: Which Expression Is Equivalent To Startroot 120 X Endroot
What is the order of operations for √(120x)?
The order of operations is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
What are some equivalent expressions to √(120x)?
Some equivalent expressions include 2√(30x), 6√(5x), and 10√(3x).
How can I use √(120x) to solve equations?
To solve equations involving √(120x), isolate the radical on one side of the equation and square both sides to eliminate the radical.
