Factoring Involving Radicals

In summary, the conversation is about finding the limit of an equation containing a radical and learning how to factor the equation to simplify it. The conversation also touches on whether or not 0 can be divided by 0 and the use of a more general formula to solve the problem. The solution involves creating a new limit as the variable approaches a certain value.
  • #1
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Homework Statement


This question is concerning a limit question. I have no problems finding limits but i need to be able to factor this equation. I need to be able to some how get rid of the (x-1)

(x^(1/6)-1)/(x-1)

The Attempt at a Solution


I ust keep ending up in a loop geting a bigger and bigger radical.
An out of curiosity can 0 be divided by 0?
 
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  • #2
Nope. Give us the actual limit, there's an easier way.
 
  • #3
No, you cannot divide by 0- not even 0! You should know, from a more general formula, that [itex]y^6- 1= (y- 1)(y^5+ y^4+ y^3+ y^2+ y+ 1)[/itex]. What happens if y= x^{1/6}?
 
  • #4
HallsofIvy said:
No, you cannot divide by 0- not even 0! You should know, from a more general formula, that [itex]y^6- 1= (y- 1)(y^5+ y^4+ y^3+ y^2+ y+ 1)[/itex]. What happens if y= x^{1/6}?
Then all that's left is to create a new limit as y approaches something. In this case its still 1 but you would need to take the 6th root of the original limit point

For example, if you wanted to do something like the limit as x approaches 8 of: [itex]\displaystyle{\frac{-x^2+ 4x^\frac{4}{3}+ x^\frac{7}{8}+ x^\frac{5}{6}- 4x^\frac{1}{2}- 4x^\frac{1}{6}}{x^\frac{2}{3}- 4}}[/itex]

You would have to again use y=x^(1/6), but take the new limit as y approaches 8^(1/6) or radical 2 of:
[tex]\displaystyle{\frac{-y^12+ 4y^8+ y^7+ y^5- 4y^3- 4y}{y^4- 4}}[/tex]
 
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1. What is factoring involving radicals?

Factoring involving radicals is a mathematical process that involves finding the factors of a number or expression that contains radicals (square roots, cube roots, etc.). This process is used to simplify the expression and make it easier to solve.

2. Why is factoring involving radicals important?

Factoring involving radicals is important because it allows us to simplify complex expressions and equations, making them easier to solve. It also helps us to better understand the relationships between numbers and expressions.

3. How do you factor an expression with radicals?

To factor an expression with radicals, you need to identify the common factors of the numbers or variables under the radicals. Then, use the rules of exponents to simplify the expression and factor out the common factors.

4. Can you factor a radical with a coefficient?

Yes, you can factor a radical with a coefficient. First, factor out the greatest perfect square from the coefficient and the number under the radical. Then, factor the remaining number under the radical using the same process as factoring without a coefficient.

5. What are some common mistakes to avoid when factoring involving radicals?

Some common mistakes to avoid when factoring involving radicals include forgetting to simplify the radicals before factoring, forgetting to factor out the greatest perfect square, and making errors in using the rules of exponents. It's important to double check your work and practice regularly to avoid these mistakes.

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