I have a quick question on square roots.

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Discussion Overview

The discussion revolves around the interpretation and simplification of a mathematical expression involving roots, specifically focusing on the notation of a fifth root and its relation to exponent notation. The context includes homework-related queries and conceptual clarifications regarding radical expressions.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents a problem involving the expression 5√x^3 and speculates that the answer might be x^3/5.
  • Another participant clarifies that the 5 is a factor, indicating that the expression should be interpreted as 5 * √(x^3).
  • A participant expresses confusion about the problem and mentions that the answer key states x^3/5, but they are unsure how to arrive at that answer.
  • Another participant corrects the interpretation, stating that the expression represents the fifth root, leading to the conclusion that it can be expressed as x^(3/5).
  • There is a suggestion that understanding these patterns is crucial for calculus, emphasizing the importance of substituting expressions into variables.
  • One participant reiterates the need for clarity in notation, explaining that √ denotes a square root, while √[n] denotes the nth root.

Areas of Agreement / Disagreement

Participants express differing interpretations of the notation, with some agreeing on the fifth root interpretation while others remain confused about the steps to simplify the expression. The discussion does not reach a consensus on the best approach to solving the problem.

Contextual Notes

There are limitations in the clarity of the problem statement, which may affect participants' understanding. The discussion also highlights the dependence on notation and the potential for misunderstanding in mathematical expressions.

DTRapture
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There's this problem on my homework that says something like 5√x3, except the 5 is like an exponent directly to the left of the square root sign. I'm not sure how to solve it, but I'm just guessing that the answer is x3/5 because, eh, who knows.
 
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The 5 is just a factor like sort(50) = 5*sqrt(2)

In your case it is 5 * sqrt(x^3)
 
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I'm confused. The problem looks like this, labeled next to the "7". I don't know the steps to simplify/solve it.

I looked at the answer key and the answer actually was x^3/5, but I don't know how to get that answer.
 
Okay that's different from what you typed. It means the 5th root not the square root. so yes it can be written as x^(3/5) or in english as x to the three fifths power.

So a square root is x^(1/2) and a cube root is x^(1/3) so a fifth root is x^(1/5) Do you see the pattern?

Since the number under the root is x^3 then what is the answer?
 
I'll assume that it's x3/5?
 
Don't assume. You need to know the answer

if its the 5th root of y and y=x^3 then what's the answer?
 
Then yeah, it is x3/5.

Like how the 7th root of y and y=x3 will be x3/7
 
Yes, I think you have it.

A lot of Calculus will depend on your ability to see these patterns and to understand how you can substitute expressions into variables...
 
DTRapture said:
View attachment 87377

I'm confused. The problem looks like this, labeled next to the "7". I don't know the steps to simplify/solve it.

I looked at the answer key and the answer actually was x^3/5, but I don't know how to get that answer.
It would be helpful if you had written the entire problem statement. According to what you showed as the answer you are neither simplifying nor solving the problem. All that you are supposed to do is rewrite the radical expression in exponent notation.
Radical notation: ##\sqrt[5]{x^3}##
Exponent notation: ##x^{3/5}##
 
  • #10
To clarify the notation \sqrt {} mean square root when there is no number. \sqrt[n] {} means nth root.
 

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